Sydney

The most recognisable building of the 20th century — Jørn Utzon's shimmering white sails rising from a promontory on the harbour, one of the world's true architectural icons. See it from the water, walk around its base at sunset, take a tour, or best of all catch a performance inside; unforgettable from every angle.

The mighty steel arch Sydneysiders call 'the Coathanger' — walk across it for free for stunning harbour views, climb the pylon lookout, or, for a bucket-list thrill, do the BridgeClimb right over the top. The classic pairing with the Opera House, and the beating heart of the harbour.

Australia's most famous beach — a broad golden arc of sand and surf backed by cafés and the promenade, packed with swimmers, surfers and sunbathers. Swim between the flags, watch the surfers, and soak up the beach culture; buzzing all summer, and lovely for the coastal walk any time of year.

One of the world's great urban coastal walks — a 6-km clifftop path from Bondi south past Tamarama, Bronte and Clovelly to Coogee, all crashing surf, rock pools and beach after beach. Do it on a sunny morning with swim stops; the sculpture-lined trail is free and endlessly gorgeous.

The best-value harbour cruise in the world is a normal public ferry — and the ride to Manly, gliding past the Opera House, the Bridge and the headlands, is the classic. Sit up top with the wind and the views; the whole harbour opens up, and it's yours for the price of an Opal-card tap.

Sydney's oldest quarter, right by the Bridge — cobbled lanes of colonial sandstone buildings, historic pubs, a weekend market and museums telling the story of the convict colony that started here. Wander the alleys, pull up at one of Australia's oldest pubs, and feel the city's beginnings.

The lush Royal Botanic Garden sweeps around the harbour's edge from the Opera House to Mrs Macquarie's Point — a carved sandstone bench with the postcard-perfect view of the Opera House and Bridge together. A gorgeous, free waterfront stroll with flying foxes in the trees; the classic photo spot.

A superb zoo on a harbour hillside, reached by a scenic ferry — meet koalas, kangaroos, platypus and Tasmanian devils, with the animals framed against a jaw-dropping view of the city skyline across the water. A brilliant family day, and the ferry-and-view combo makes it special even for grown-ups.

The buzzy western waterfront, made for a family day — the excellent SEA LIFE aquarium and Wild Life zoo, the maritime museum, restaurants around the water, and the sleek Barangaroo bars and park next door. Lively and central; come for the attractions, the harbourside dining and the evening lights.

Sydney's best eating and drinking is in the inner-city terraces of Surry Hills and Darlinghurst — small bars, natural-wine spots, laneway restaurants and buzzing pubs, a world from the touristy harbour. Bar-hop the leafy streets and graze the acclaimed kitchens; this is where locals go out.

The world's most photographed swimming pool — a spectacular ocean pool at the southern end of Bondi where waves crash over the edge, with a swim club and a chic restaurant-bar above. Do laps in the sea pool with that view, or just have a drink on the terrace watching the surfers; peak Sydney.

A long, laid-back surf beach on the northern side, reached by the lovely ferry — pine-lined promenade, gentle surf, and a walk over to the little coves and the harbourside on the other side of the peninsula. More relaxed and family-friendly than Bondi, and the ferry there is half the pleasure.

The state's superb art gallery on the edge of the Domain parkland — Australian and Aboriginal art, European masters and a striking new wing, all free to enter. A cool, cultured couple of hours a short walk from the Opera House; the Aboriginal art collection alone is worth the visit.

Australia is a coffee superpower and Sydney takes brunch seriously — a velvety flat white and a plate of smashed avo, ricotta hotcakes or a big breakfast at a buzzing café is a local ritual. Do a long, sunny weekend brunch in Surry Hills or by the beach; the café culture here is world-beating.

The golden-topped tower spiking the CBD skyline has the highest observation deck in the city — a 360° view over the harbour, the beaches and out to the Blue Mountains, with a glass-floored SkyWalk for the brave. The best way to grasp the geography of the harbour city; go on a clear day.