Sydneysiders adore their giant 'coathanger'. Opened in 1932, this majestic structure spans the harbour at one of its narrowest points. The best way to experience the bridge is on foot – don't expect much of a view crossing by car or train. Stairs climb up the bridge from both shores, leading to a footpath running the length of the eastern side. You can climb the southeastern pylon to the Pylon Lookout or ascend the great arc on the wildly popular BridgeClimb.

The harbour bridge is a spookily big object – moving around town you’ll catch sight of it in the corner of your eye, sometimes in the most surprising of places. At 134m high, 1149m long, 49m wide and weighing 52,800 tonnes, it's the largest and heaviest (but not the longest) steel arch in the world.

The two halves of chief engineer JJC Bradfield’s mighty arch were built outwards from each shore. In 1930, after nine years of merciless toil by 1400 workers, the two arches were only centimetres apart when 100km/h winds set them swaying. The coathanger hung tough and the arch was finally bolted together.

Perhaps Sydney poet Kenneth Slessor said it best: ‘Day and night, the bridge trembles and echoes like a living thing.’

Sydney Harbour National Park protects large swathes of bushland around the harbour shoreline, plus several harbour islands. In among the greenery you’ll find walking tracks, scenic lookouts, Aboriginal carvings, beaches and a handful of historic sites. The park incorporates South Head ( GOOGLE MAP ; www.nationalparks.nsw.gov.au; Cliff St; h5am-10pm; fWatsons Bay) and Nielsen Park on the south side of the harbour, but most of the park is on the North Shore – including Bradleys Head, Middle Head, Dobroyd Head and North Head.

The views from the top of the Harbour Bridge's southeast pylon are awesome, and museum exhibits here explain how the bridge was built. The pylons may look as though they’re shouldering all the weight, but they’re largely decorative – right down to their granite facing. Enter via the bridge stairs on Cumberland St.

Studded with photogenic industrial relics, convict architecture and art installations, fascinating Cockatoo Island (Wareamah) opened to the public in 2007 and now has regular ferry services, a campground, rental accommodation, a cafe and a bar. Information boards and audio guides ($5) explain the island's time as a prison, shipyard and naval base.

A spooky tunnel passes clear through the middle of the island and you can also explore the remains of the prison. During WWII most of the old sandstone buildings were stripped of their roofs and converted into bomb shelters. Solitary confinement cells were unearthed here recently after being filled in and forgotten in the 1890s.

Goat Island, west of the Harbour Bridge, has been a shipyard, quarantine station and gunpowder depot in its previous lives. Heritage tours are offered for groups of 20 or more (see the national parks website for details).

Called Mat-te-wan-ye (rocky island) by the Gadigal people, in colonial times the small fortified island off Mrs Macquaries Point was a sorry site of suffering, used to isolate recalcitrant convicts. It was nicknamed ‘Pinchgut’ for its meagre rations. Fears of a Russian invasion during the mid-19th-century Crimean War led to its fortification. The NPWS offers tours of the Martello tower (cheaper if prebooked with your ferry ticket), although plenty of people just pop over to visit the cafe.

Both Captain Cook Cruises and Manly Fast Ferry have several services per day heading to the island from Darling Harbour and Circular Quay.

Little Shark Island, off Rose Bay, makes a great picnic getaway. There's not a lot here except for toilets and drinking water – and at 250m by 100m, you'll soon have explored every inch of it. Captain Cook Cruises runs four ferries per day to the island from Circular Quay (jetty 6) and Darling Harbour (pier 26).

High on the hill inside the old Fort St School (1856), the SH Ervin Gallery exhibits invariably rewarding historical and contemporary Australian art. Annual mainstays include the Salon des Refusés (alternative Archibald Prize entries) and the Portia Geach Memorial Award. There’s a cafe here, too.

Built in the 1850s, Sydney’s copper-domed, Italianate observatory squats atop pretty Observatory Hill, overlooking the harbour. Inside is a collection of vintage apparatus, including Australia’s oldest working telescope (1874). Also on offer are audiovisual displays, including Aboriginal sky stories and a virtual reality 3D Theatre (www.sydneyobservatory.com.au; adult/child $10/8; h2.30pm & 3.30pm daily, plus 11am & noon Sat & Sun; dCircular Quay). Bookings are essential for night-time stargazing sessions (adult/child $18/12).

If you’re feeling more earthly, Observatory Hill is great for a picnic. Studded with huge Moreton Bay fig trees, the grassy hilltop buzzes with sweaty hill-climbing joggers, lunchtime CBD escapees and travellers taking time out from the Rocks below. The hill was the site of the colony’s first windmill (1796), which ground wheat until someone stole its canvas sails and the structure collapsed.

Dating from 1844, this diminutive terrace of four houses and a shop selling historical wares is a fascinating time capsule of life in the Rocks since colonial times. After you watch a short film about the people who lived here, a guide will take you through the claustrophobic homes, which are decorated to reflect different periods in their histories.

Divided into four chronological displays – Warrane (pre-1788), Colony (1788–1820), Port (1820–1900) and Transformations (1900 to the present) – this excellent museum digs deep into the Rocks’ history and leads you on an artefact-rich tour. Sensitive attention is given to the Rocks’ original inhabitants, the Gadigal people.

One of country's best and most challenging galleries, the MCA is a showcase for Australian and international contemporary art. Aboriginal art features prominently. The fab Gotham City–style art deco building bears the wounds of a redevelopment that has grafted on additional gallery space and a rooftop cafe/sculpture terrace – and ruined the George St facade in the process.

Volunteer-led guided tours are offered at 11am and 1pm daily, and at 7pm Thursdays and 3pm on weekends.

This attractive sandstone church (1844) was built on land donated by William Davis, an Irishman transported for his role in the 1798 uprisings. Inside it’s incredibly quiet, which makes the brass altar, the stained-glass windows and the colourful statues of St Patrick, St Joan of Arc and St Michael (complete with dragon) seem even more striking. Guided tours are infrequent but worthwhile; visit the website for details.

Davis' home (on the site of the chapel-turned-cafe) was arguably the first Catholic chapel in Australia; it was used for clandestine devotions and secretly housed a consecrated host after the colony’s only Catholic priest was deported in 1818.

This elegant harbourside edifice (1885) houses a bar, Cafe Sydney ( MAP GOOGLE MAP ; %02-9251 8683; www.cafesydney.com; L5, Customs House, 31 Alfred St; mains $38-39; hnoon-11pm Mon-Fri, 5-11pm Sat, noon-3.30pm Sun; dCircular Quay), on the top floor, and the three-level Customs House Library ( MAP GOOGLE MAP ; %02-9242 8555; 31 Alfred St; h10am-7pm Mon-Fri, 11am-4pm Sat & Sun; dCircular Quay), which has a great selection of international newspapers and magazines, internet access and interesting temporary exhibitions. In the lobby, look for the swastikas in the tiling (and the plaque explaining their symbolism), and a fascinating 1:500 model of the inner city under the glass floor.

Occupying the old Water Police Station (1858), this mildly unnerving museum documents the city's dark and disreputable past through old police photographs and an often macabre collection of exhibits.

Designed by Danish architect Jørn Utzon, this World Heritage-listed building is Australia's most recognisable landmark. Visually referencing the billowing white sails of a seagoing yacht (but described by some local wags as more accurately resembling the sexual congress of turtles), it's a commanding presence on Circular Quay. The complex comprises five performance spaces where dance, concerts, opera and theatre are staged.

The best way to experience the building is to attend a performance, but you can also take a one-hour guided tour, conducted in a variety of languages. There's also a two-hour 'access all areas' backstage tour ($165), which departs at 7am and includes breakfast in the Green Room.

These expansive gardens are the city's favourite picnic destination, jogging route and snuggling spot. Bordering Farm Cove, east of the opera house, the gardens were established in 1816 and feature plant life from Australia and around the world. They include the site of the colony's first paltry vegetable patch, but their history goes back much further than that; long before the convicts arrived, this was an initiation ground for the Gadigal people.

Free 1½-hour guided walks depart at 10.30am daily. From November to March there's an additional hour-long tour at 1pm on weekdays. Book ahead for an Aboriginal Heritage Tour (%02-9231 8134; adult/child $37/17; h10am Fri), which covers local history, traditional plant uses and bush-food tastings.

Encased in English-style grounds within the Royal Botanic Gardens, this Gothic sandstone mansion (built 1837–43) is the official residence of the Governor of NSW. It's also used for hosting visiting heads of state and royalty. The interior can only be accessed on a free guided tour; collect your ticket from the gatehouse.

Adjoining the Royal Botanic Garden but officially part of the Domain, Mrs Macquaries Point forms the northeastern tip of Farm Cove and provides beautiful views over the bay to the Opera House and city skyline. It was named in 1810 after Elizabeth, Governor Macquarie’s wife, who ordered a seat chiselled into the rock from which she could view the harbour. Mrs Macquaries Chair, as it's known, remains to this day.

Administered by the Royal Botanic Gardens, the Domain is a large grassy tract east of Macquarie St, set aside by Governor Phillip in 1788 for public recreation. Phillip’s intent rings true: today’s city workers use the space to work up a sweat or eat their lunch. Large-scale public events are also held here.

Sculptures dot the park, including a reclining Henry Moore figure, and Brett Whiteley’s Almost Once (1991) − two giant matches, one burnt − rising from the ground near the Art Gallery of NSW.

On the lawn in front of the gallery you can listen to religious zealots, nutters, political extremists, homophobes, hippies and academics express their earnest opinions at the by turns entertaining and enraging Speakers’ Corner ( GOOGLE MAP ; www.speakerscorner.org.au; Art Gallery Rd; h2-5pm Sun; dSt James). Some of them have something interesting to say; most are just plain mad. Either way, it makes for an interesting afternoon. BYO soapbox.

With its classical Greek frontage and modern rear end, this much-loved institution plays a prominent and gregarious role in Sydney society. Blockbuster international touring exhibitions arrive regularly and there's an outstanding permanent collection of Australian art, including a substantial Indigenous section. The gallery also plays host to lectures, concerts, screenings, celebrity talks and children's activities. A range of free guided tours is offered on different themes and in various languages; enquire at the desk or check the website.

Among the State Library's over five million tomes are James Cook’s and Joseph Banks’ journals and William Bligh’s log from the mutinous HMAV Bounty. It's worth dropping in to peruse the temporary exhibitions in the galleries, and the elaborately sculpted bronze doors and grand atrium of the neoclassical Mitchell Wing (1910); note the map of Abel Tasman’s journeys in the mosaic floor. The main reading room is an elegant temple of knowledge clad in milky marble.

Outside, on the Macquarie St side of the building, is a sculpture of explorer Matthew Flinders; look for his intrepid cat Trim on the windowsill behind.

Twin of the nearby Mint, the venerable Parliament House (1816) has been home to the Parliament of New South Wales since 1829, making it the world’s oldest continually operating parliament building. And like the Mint, its front section (which now blends into a modern addition on the eastern side) was part of the Rum Hospital (built in exchange for a monopoly on the rum trade).

You need to pass through a metal detector to access the inner sanctum, where you can check out art exhibitions in the lobby and the historical display in the wood-panelled Jubilee Room. On nonsitting days both assembly chambers are open, but when Parliament is sitting, you’re restricted to the Public Gallery.

Convict architect Francis Greenway designed this squarish, decorously Georgian structure (1819) as convict quarters. Between 1819 and 1848, 50,000 men and boys did time here, most of whom had been sentenced by British courts to transportation to Australia for property crime. It later became an immigration depot, a women’s asylum and a law court. These days it’s a fascinating (if not entirely cheerful) museum, focusing on the barracks’ history and the archaeological efforts that helped reveal it.

Built from convict-made bricks, Sydney’s oldest church (1819) is widely considered to be architect Francis Greenway's masterpiece. It was originally designed as a courthouse, but the brief changed and the cells became the crypt. Check out the dark-wood choir loft, the sparkling copper dome, the crypt and the 1950s stained-glass ‘Creation Window’.

Formal but much-loved Hyde Park has manicured gardens and a tree-formed tunnel running down its spine which looks particularly pretty at night, illuminated by fairy lights. The park’s northern end is crowned by the richly symbolic art deco Archibald Memorial Fountain ( MAP GOOGLE MAP ; dSt James), featuring Greek mythological figures, while at the other end is the Anzac Memorial.

Built to last, this 106m-long Gothic Revival–style cathedral was begun in 1868, consecrated in 1905 and substantially finished in 1928, but the massive, 75m-high spires weren’t added until 2000. The crypt has an impressive terrazzo mosaic floor depicting the Creation, inspired by the Celtic-style illuminations of the Book of Kells.

Fronted by the Pool of Remembrance, this dignified art deco memorial (1934) commemorates the soldiers of the Australia and New Zealand Army Corps (Anzacs) who served in WWI. The interior dome is studded with 120,000 stars – one for each New South Welsh man and woman who served. These twinkle above Rayner Hoff’s poignant sculpture Sacrifice, featuring a naked soldier draped over a shield and sword. There's also a small museum downstairs where a 13-minute film screens every 30 minutes.

Built on the site of Sydney’s first (and infamously pungent) Government House, the MoS is a fragmented, story-telling museum, which uses state-of-the-art installations to explore the city’s people, places, cultures and evolution. The history of the Indigenous Eora people is highlighted – touching on the millennia of continuous occupation of this place. Be sure to open some of the many stainless-steel and glass drawers (they close themselves).

Studded with imposing edifices, long, lean Martin Place was closed to traffic in 1971, forming a terraced pedestrian mall complete with fountains and areas for public gatherings. It's the closest thing to a main civic square that Sydney has. In 2014 the Lindt cafe at 53 Martin Place was the site of a 16-hour siege, ending in the death of two hostages and the gunman. At the time of writing, a permanent memorial to the victims was being planned.

As iconic in its time as the Opera House, GPO Sydney ( MAP GOOGLE MAP ; www.gposydney.com; 1 Martin Pl; dMartin Place), built in 1874, is a beautiful colonnaded Victorian palazzo that was once Sydney’s General Post Office. It has since been gutted, stabbed with office towers and transformed into the Westin Sydney hotel, swanky shops, restaurants and bars. Inspired by Italian Renaissance palaces, architect James Barnet caused a minor fracas by basing the faces carved on the sandstone facade on local identities. Queen Victoria dominates the central white-marble statuary, surrounded by allegorical figures. Under a staircase in the basement there is a small historical display and a pipe housing the dribbling remnants of the Tank Stream.

Built in 1916, 12-storey 5 Martin Place ( MAP GOOGLE MAP ; www.5martinplace.com.au; 5 Martin Pl; dMartin Place) was Australia’s first steel-framed ‘skyscraper’. At the time of writing, it was in the process of a major redevelopment, with a glass tower being grafted on to it.

A Commonwealth Bank branch ( MAP GOOGLE MAP ; 48 Martin Pl; dMartin Place) has taken over the old State Savings Bank building: it’s a beaut example of interwar beaux-arts architecture, featuring green-marble Ionian columns and an enclosed brass-and-marble teller area.

Near the George St end of Martin Place you’ll find the Cenotaph, commemorating Australia’s war dead. Abutting Martin Place on George St is the former Commercial Banking Corporation of Sydney – an impressive marbled edifice, worth a look if you’re passing by.

The 309m-tall Sydney Tower (built 1970–1981) offers unbeatable 360-degree views from the observation level 250m up – and even better ones for the daredevils braving the Skywalk on its roof. The visit starts with the 4D Experience – a short 3D film giving you a bird's-eye view (a parakeet's to be exact) of city, surf, harbour and what lies beneath the water, accompanied by mist sprays and bubbles; it's actually pretty darn cool.

The heritage-listed Great Synagogue (1878) is the spiritual home of Sydney’s oldest Jewish congregation, established in 1831. It’s considered the Mother Synagogue of Australia and is architecturally the most important in the southern hemisphere, combining Romanesque, Gothic, Moorish and Byzantine elements. Tours include the AM Rosenblum Museum’s artefacts and a video presentation on Jewish beliefs, traditions and history in Australia.

Unbelievably, this High Victorian masterpiece (1898) was repeatedly slated for demolition before it was restored in the mid-1980s. Occupying an entire city block on the site of the city’s first markets, the QVB is a Venetian Romanesque temple to the gods of retail.

Sure, the 200 speciality shops are great, but check out the wrought-iron balconies, the Byzantine copper domes, the stained-glass shopfronts, the mosaic floors, the replica crown jewels, the ballroom, the tinkling baby grand and the hyperkitsch animated Royal Clock (featuring the Battle of Hastings and an hourly beheading of Charles I). Informative 45-minute tours (11.30am Tuesday, Thursday and Saturday) depart from the concierge desk on the ground floor.

Outside there’s an imposing statue of Queen Vic herself. Nearby is a wishing well featuring a bronze replica of her beloved pooch, Islay, which disconcertingly speaks in the baritone voice of former radio rabble-rouser John Laws.

Mansard roofs, sandstone turrets, wrought-iron trimmings and over-the-top balustrades: the French Second Empire wedding-cake exterior of the Town Hall (built 1868–89) is something to behold. Unless there's something on, you can explore the halls off the main entrance. The wood-lined concert hall has a humongous pipe organ with nearly 9000 pipes; it was once the largest in the world. It's used regularly for recitals, some of which are free.

With a discordant soundtrack of blaring Canto pop, Dixon St is the heart and soul of Chinatown: a narrow, shady pedestrian mall with a string of restaurants and their urgently attendant spruikers. The ornate dragon gates (paifang) at either end of the street are topped with fake bamboo tiles, golden Chinese calligraphy (with English translations), ornamental lions to keep evil spirits at bay and a fair amount of pigeon poo.

This is actually Sydney’s third Chinatown: the first was in the Rocks in the late 19th century before it moved to the Darling Harbour end of Market St. Dixon St’s Chinatown dates from the 1920s. Look for the fake-bamboo awnings guarded by dragons, dogs and lions, and kooky upturned-wok lighting fixtures.

On Hay St, the surreal Golden Water Mouth ( MAP GOOGLE MAP ; Hay St; dTown Hall) sculpture drips with gilt and water. Formed from a eucalyptus trunk from Condobolin, the destination of many gold-rush-era Chinese, its feng shui is supposed to promote positive energy and good luck. A little further down Hay St, Paddy’s Markets ( MAP GOOGLE MAP ; www.paddysmarkets.com.au; 9-13 Hay St; h10am-6pm Wed-Sun; dCentral) fills the lower level of a hefty brick building. It started out in the mid-19th century with mainly European traders, but the tightly packed market stalls are more evocative of present-day Vietnam these days.

As well as regular wall-mounted tanks and ground-level enclosures, this impressive complex has two large pools that you can walk through, safely enclosed in Perspex tunnels, as an intimidating array of sharks and rays pass overhead. Other highlights include clownfish (howdy Nemo), platypuses, moon jellyfish (in a disco-lit tube), sea dragons and the swoon-worthy finale: the two-million-litre Great Barrier Reef tank.

The aquarium's two dugongs were rescued after washing up on Queensland beaches. Attempts to return them to the wild failed, so the Dugong Island enclosure was built to house them. As sad as it is to see such large marine mammals in captivity, it offers a fascinating and rare opportunity to get close to them.

Needless to say, kids love this place; arrive early to beat the crowds. It's cheaper to book online.

Complementing its sister and neighbour, Sea Life, this large complex houses an impressive collection of Australian native reptiles, butterflies, spiders, snakes and mammals (including kangaroos and koalas). The nocturnal section is particularly good, bringing out the extrovert in the quolls, potoroos, echidnas and possums. As interesting as Wild Life is, it's not a patch on Taronga Zoo. Still, it's worth considering as part of a combo with Sea Life, or if you're short on time. Tickets are cheaper online.

In this celebrity-obsessed age, it's hardly surprising that Madame Tussauds' hyperrealistic waxwork dummies are just as popular now as when the eponymous madame lugged her macabre haul of French revolution death masks to London in 1803. Where else do mere mortals get to strike a pose with Hugh Jackman and cosy up to Kylie?

The first vaguely tasteful development in Darling Harbour, Cockle Bay Wharf occupies the harbour’s cityside frontage as far as Pyrmont Bridge. Its sharp, contemporary angles are softened by the use of timber and whimsical sculptures (we particularly like the jaunty dancing storks).

Flanked by the new Darling Walk development, this grassy circle on Darling Harbour’s southern rump is set up for family fun. Sunbakers and frisbee-throwers occupy the lawns; tourists dunk their feet in fountains on hot summer afternoons; and there’s an excellent children’s playground with a 21m flying fox.

Built according to Taoist principles, the Chinese Garden of Friendship is usually an oasis of tranquillity – although construction noise from Darling Harbour's redevelopment can intrude from time to time. Designed by architects from Guangzhou (Sydney’s sister city) for Australia’s bicentenary in 1988, the garden interweaves pavilions, waterfalls, lakes, paths and lush plant life.

Beneath an Utzon-like roof (a low-rent Opera House?), the Maritime Museum sails through Australia’s inextricable relationship with the sea. Exhibitions range from Indigenous canoes to surf culture, to the navy. Entry includes free tours and there are kids' activities on Sundays. The ‘big ticket’ (adult/child $27/16) includes entry to the vessels moored outside, including the submarine HMAS Onslow, the destroyer HMAS Vampire and an 1874 square rigger, the James Craig, which periodically offers sailing trips. Normally a replica of Cook’s Endeavour also drops anchor.

This piscatorial precinct on Blackwattle Bay shifts over 15 million kilograms of seafood annually, and has retail outlets, restaurants, a sushi bar, an oyster bar and a highly regarded cooking school. Chefs, locals and overfed seagulls haggle over mud crabs, Balmain bugs, lobsters and slabs of salmon at the daily fish auction, which kicks off at 5.30am weekdays. Check it out on a behind-the-scenes tour (adult/child $30/10).

A short walk from Darling Harbour, this science and design museum whirs away inside the former power station for Sydney’s defunct, original tram network. High-voltage interactive demonstrations wow school groups with the low-down on how lightning strikes, magnets grab and engines growl. It's a huge hit with kids but equally popular with adults, touching on subjects such as fashion and furniture design.

Occupying the site of an old brewery, this work-in-progress residential and shopping development will eventually cover 6500 sq metres, and is already revitalising the central fringe suburb of Chippendale. Most impressive is Jean Nouvel's award-winning, vertical garden–covered tower, One Central Park (2013, 117m). The cantilevered roof has been designed to reflect sunlight onto the greenery below. A striking new Frank Gehry building is being built on the University of Technology campus across Broadway.

If you're an art lover or a bit of a Mad Hatter, this particular rabbit hole will leave you grinning like a Cheshire Cat. There are so many works in this private collection of cutting-edge, contemporary Chinese art, that only a fraction can be displayed at one time. Who knew that the People's Republic was turning out work that was so edgy, funny, sexy and idiosyncratic?

Acclaimed local artist Brett Whiteley (1939–92) lived fast and without restraint. His hard-to-find studio (look for the signs on Devonshire St) has been preserved as a gallery for some of his best work. At the door is a miniature of his famous sculpture Almost Once, which you can see in all its glory in the Domain.

This natural-history museum, established just 40 years after the First Fleet dropped anchor, has endeavoured to shrug off its museum-that-should-be-in-a-museum feel by jazzing things up a little. Hence dusty taxidermy has been interspersed with video projections and a terrarium with live snakes, while dinosaur skeletons cosy up to life-size recreations. Yet it's the more old-fashioned sections that are arguably the most interesting – the large collection of crystals and precious stones, and the hall of skeletons.

Created largely as a Holocaust memorial, this museum examines Australian Jewish history, culture and tradition, from the time of the First Fleet (which included 16 known Jews), to the immediate aftermath of WWII (when Australia became home to the greatest number of Holocaust survivors per capita, after Israel), to the present day. Allow at least two hours to take it all in. Free 45-minute tours leave at noon on Monday, Wednesday, Friday and Sunday.

A former wool and cargo dock, this beautiful Edwardian wharf faced oblivion for decades before a 2½ year demolition-workers’ green ban on the site in the late 1980s saved it. It received a huge sprucing up in the late 1990s and has emerged as one of Sydney’s most exclusive eating, drinking, sleeping and marina addresses.

Now dwarfed by 20th-century apartments, Colonial Secretary Alexander Macleay's elegant Greek Revival mansion was one of the finest houses in the colony when it was completed in 1839. The architectural highlight is an exquisite oval entrance saloon with a curved and cantilevered staircase.

A manicured vision from the peak of the British Empire (built 1841 to 1848), these Georgian army barracks have been called the finest of their kind in the colonies. It's still an active army base, so entry is only possible on a free guided tour. You'll usually get to see a marching band perform (weather permitting) and afterwards you can visit the on-site Army Museum of NSW (admission $2). Good disabled access.

Opened to much architectural acclaim in 2008, this impressive park makes use of Paddington's long-abandoned 1866 water reservoir, incorporating the brick arches and surviving chamber into an interesting green space featuring a sunken garden, a pond, a boardwalk and lawns. They've even preserved some of the graffiti dating from the many years when it was boarded up and abandoned to feral cats and stealthy spray-can artists.

Scratched out of the sand in 1888 in grand Victorian style, Sydney’s biggest park is a rambling 189-hectare expanse full of horse riders, joggers, cyclists and in-line skaters. During summer Moonlight Cinema attracts the crowds.

Not really a pool at all, family-friendly Murray Rose (named after a champion Olympic swimmer) is the closest swimming spot to the city – as such, it attracts an urbane cross-section of inner-eastern locals. A boardwalk runs around the top of the shark net, and there are two sought-after floating pontoons.

Something of a hidden gem, this gorgeous harbourside park with a sandy beach was once part of the then 206-hectare Vaucluse House estate. Secluded beneath the trees is Greycliffe House, a gracious 1851 Gothic sandstone pile (not open to visitors), which serves as the headquarters of Sydney Harbour National Park.

Construction of this imposing, turreted specimen of Gothic Australiana, set amid 10 hectares of lush gardens, commenced in 1805, but the house was tinkered with into the 1860s. Decorated with beautiful European period pieces including Bohemian glass, heavy oak Jacobethan furniture and Meissen china, the house offers visitors a rare glimpse into early Sydney colonial life, as lived by the well-to-do.

The only things to distract you from serious beach time at divine Milk Beach are seaplanes and the glistening Sydney skyline. With wow-worthy harbour views and limited access down a steep bush path, this isolated stretch of sand at the base of Hermit Bay is still one of the city's best kept secrets. Heritage-listed Strickland House is out back, and clear, warm waters are in front, at this tiny parcel of harbourside paradise.

Immediately north of Watsons Bay, this small swimming beach is popular with both families and topless sunbathers. When Governor Phillip realised Botany Bay didn't cut it as a site for a convict colony, he sailed north into Sydney Harbour, dropped anchor and sank his boots into Camp Cove's gorgeous golden sand on 21 January 1788.

Definitively Sydney, Bondi is one of the world’s great beaches: ocean and land collide, the Pacific arrives in great foaming swells, and all people are equal, as democratic as sand. It’s the closest ocean beach to the city centre (8km away), has consistently good (though crowded) waves, and is great for a rough-and-tumble swim (the average water temperature is a considerate 21°C). If the sea’s angry, try the child-friendly saltwater sea baths at either end of the beach.

Two surf clubs – Bondi and North Bondi – patrol the beach between sets of red-and-yellow flags, positioned to avoid the worst rips and holes. Thousands of unfortunates have to be rescued from the surf each year (enough to make a TV show about it), so don’t become a statistic – swim between the flags.

Surfers carve up sandbar breaks at either end of the beach; it’s a good place for learners, too. Prefer wheels to fins? There’s a skate ramp ( MAP GOOGLE MAP ; Queen Elizabeth Dr; g380) at the beach’s southern end. If posing in your budgie smugglers (Speedos) isn’t having enough impact, there’s an outdoor workout area ( MAP GOOGLE MAP ; Queen Elizabeth Dr; g380) near the North Bondi Surf Club. Coincidentally (or perhaps not), this is the part of the beach where the gay guys hang out.

Bondi Pavilion has changing rooms, lockers, cafes and a gelato shop. Ice-cream vendors also strut the sand in summer. At the beach’s northern end there’s a grassy spot with coin-operated barbecues. Booze is banned on the beach.

Surrounded by high cliffs, Tamarama has a deep tongue of sand with just 80m of shoreline. Diminutive, yes, but ever-present rips make Tamarama the most dangerous patrolled beach in New South Wales; it’s often closed to swimmers. It’s hard to picture now, but between 1887 and 1911 a roller coaster looped out over the water as part of an amusement park.

A winning family-oriented beach hemmed in by sandstone cliffs and a grassy park, Bronte lays claims to the title of the oldest surf lifesaving club in the world (1903). Contrary to popular belief, the beach is named after Lord Nelson, who doubled as the Duke of Bronte (a place in Sicily), and not the famous literary sorority. There’s a kiosk and a changing room attached to the surf club, and covered picnic tables near the public barbecues.

It might seem odd, but this concrete-edged ocean channel is a great place to swim, sunbathe and snorkel. It’s safe for the kids, and despite the swell surging into the inlet, underwater visibility is great. A beloved friendly grouper fish lived here for many years until he was speared by a tourist. Bring your goggles, but don’t go killing anything…

On the other side of the car park is the entrance to the Gordons Bay Underwater Nature Trail, a 500m underwater chain guiding divers past reefs, sand flats and kelp forests.

Bondi without the glitz and the posers, Coogee (locals pronounce the double o as in the word ‘took’) has a deep sweep of sand, historic ocean baths and plenty of green space for barbecues and frisbee hurling. Between the world wars, Coogee had an English-style pier, with a 1400-seat theatre and a 600-seat ballroom…until the surf took it.

Australia’s oldest tertiary institution (1850) has over 49,000 students and even boasts its own postcode. You don’t need to have a PhD to grab a free campus map and wander around. Flanked by two grand halls that wouldn’t be out of place in Harry Potter’s beloved Hogwarts, the Quadrangle has a Gothic Revival design that tips its mortarboard towards the stately colleges of Oxford. It's well worth seeking out the august collections of the Nicholson Museum, University Art Gallery ( MAP GOOGLE MAP ; www.sydney.edu.au/museums; Science Rd; h10am-4.30pm Mon-Fri, noon-4pm 1st Sat of month; g422-440) and Macleay Museum.

Within the University of Sydney's quadrangle, this museum is a must-see for ancient-history geeks. Inside is an amazing accumulation of Greek, Roman, Cypriot, Egyptian and Near Eastern antiquities, including Padiashaikhet the mummy. It was founded in 1860 by orphan-made-good Sir Charles Nicholson, a key figure in the establishment of both the university and the Australian Museum.

The University of Sydney's natural history museum is the oldest of its kind in Australia, having its roots in the collection of the Macleay family (of Elizabeth Bay House fame). There's also a historic photographic collection and an early assemblage of Aboriginal, Torres Strait and Pacific Island cultural material.

Built between 1880 and 1889, this intriguing group of huge Victorian-era workshops was part of the Eveleigh Railyards. The rail workers chugged out in 1988 and in 2007 the artists pranced in. It's now home to various avant-garde arts and performance projects, and there's usually something interesting to check out.

Full of dog walkers, kite flyers and stragglers from last night’s party, 40-hectare Sydney Park is a great place to chill out. From the bald hilltop you can see the city rising like a volcanic island from a sea of suburbia, while to the south there are views over the airport to Botany Bay. Much of the land has been reclaimed from swamps, clay pits and brickworks.