Sydney

Striking, unique, curvalicious – is there a sexier building on the planet? Seeing such a recognisable object for the first time is always an odd experience. Depending on where you stand, the Opera House can seem smaller or bigger than you think it's going to be. It confounds expectations but is never disappointing. Most of all, it's a supremely practical building and what goes on inside (theatre, dance, concerts) can be almost as interesting as the famous exterior. It's a magnificent place.

Spread out around the harbour, this unusual national park offers a widely varied set of experiences, all with a blissful watery view. In this park, it's equally possible to separate yourself from civilisation or to be surrounded by traffic. It incorporates harbour islands, secluded beaches, ancient rock art, lighthouses, untouched headlands and, right in the middle of the city, a historic cottage. You can kayak into otherwise inaccessible coves, plan your own ferry-hike combinations or cycle along well-tended paths. Pack a picnic and disappear along the bushy trails.

An essential Sydney experience, Bondi Beach offers fabulous opportunities for lazing on the sand, lingering in cafes, carving up the surf, splashing about in the shallows and swimming in sheltered pools. Every summer the world comes to Bondi, and what a wonderful world it is. The tightly arranged beach towels form a colourful mosaic, and a walk to the water can reveal a multitude of accents and languages. After dark, the action shifts to accomplished restaurants, quirky bars and bustling pubs.

Like the Opera House, Sydney's second-most-loved construction inhabits the intersection of practicality and great beauty. The centrepiece of the city's biggest celebrations, the bridge is at its best on New Year's Eve when it erupts in pyrotechnics and the image is beamed into lounge rooms the world over. Its sheer size is impressive, and as you explore Sydney there's always some intriguing new view of it. The views it provides are magnificent, whether you're walking over it or joining a BridgeClimb expedition up and over its central rainbow of steel.

Although the bustle of the city couldn't be closer, these spacious gardens right in the centre of town are superbly tranquil – the only visible traffic being the little road train that whisks people around and the purposeful procession of ferries on the harbour. Whether you're content to spread out a picnic on the lawn, stroll with glorious harbour perspectives or study the signs on the botanical specimens, it's an idyllic place in which to hang around for an hour or two.

The Art Gallery of NSW's stately neoclassical building doesn't divulge the exuberance of the collection it contains. Step inside and a colourful world of creativity opens up, offering portals into Sydney's history, Indigenous Australian heritage, the outback and distant lands. There's certainly nothing stuffy about the place. All are welcome (including children, who are particularly well catered for), admission is free, and complimentary guided tours help to break down any lingering belief that art is the province of a knowledgeable elite.

Eat to the beat of a city resonant with the flavours of the multitude of cultures that inhabit it. Sydney's dining scene has never been more diverse, inventive and downright exciting. Sure, it can be pretentious, faddish and a little too obsessed with celebrity chefs, but it wouldn't be Sydney if it weren't. It's assuredly not a case of style over substance – Sydney's quite capable of juggling both. Fine diners like Quay are standouts, but cheap noodles with BYO wine somewhere in the Inner West is another highlight.

Australia's convict history began here with a squalid canvas shanty town on a rocky shore. Its raucous reputation lives on in atmospheric lanes lined with historic buildings, more than a few of them still operating as pubs. Sure, the place is overrun with tacky, overpriced stuffed-koala stores and package tourists, but there are some great museums here as well. When it all gets too much, head through the convict-hewn Argyle Cut to the less frantically commercial Millers and Dawes Points, and lovely Walsh Bay.

A day trip to Taronga Zoo offers so much more than the animals: running the gauntlet of didjeridu players and living statues at Circular Quay; the ferry ride past the Opera House and out into the harbour; the cable car from the wharf to the top gate; the ever-present views of the city skyline as you make your way between the enclosures. And to cap it all off, the zoo is excellent too, with the chance to meet all those weird and wonderful Australian creatures.

It inevitably comes as a surprise to stumble across an art form that's so ancient in such a modern city, yet Sydney is built on top of a giant gallery. Until recently not much attention was paid to such things and much was covered over or destroyed. But with dot paintings from distant deserts being celebrated, Sydneysiders have started to wake up to the treasure trove in their own backyard. Look for it on headlands around the harbour and on the coast and in nearby national parks.