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Conquer your fear of heights and scale the iconic Sydney Harbour Bridge. After suiting up, you'll ascend the arches of ‘the coathanger’ and be rewarded with stunning 360-degree views of the city stretching as far as the Blue Mountains.

Enjoy ballet, comedy, musical theatre and, of course, opera at one of Sydney's most recognisable tourist attractions. Alternatively, take a tour of the Unesco World Heritage site to learn its architectural secrets, or visit one of the onsite restaurants and relax with harbour views.

Catching the ferry to Manly is one of the quintessential things to do in Sydney. The picturesque seaside town offers one of the city's best beaches, a surf school, lively pedestrianised shopping area and plenty of restaurants and cafes.

Wander down the cobbled lanes of The Rocks and soak in the historical atmosphere – this was the first site of European settlement. The Rocks is also bursting with markets, art galleries and great dining options by day, with classy bars to visit when the sun goes down.

Every Saturday, vendors at King’s Cross Farmers Market hawk fresh organic produce and ready-to-eat delicacies, from cheese and charcuterie to cakes and pastries. With plenty of outdoor seating, it’s the perfect place to while away an afternoon and soak up the neighbourhood’s charm.

Once a criminal heartland, Surry Hills has become known for quirky cafes, bars, vintage shops – and a thriving gallery scene. Check out the Brett Whiteley Studio, the former home and workspace of the 20th-century avant-garde artist. Or visit M2 for modern artworks ranging from photography to performance.

A short ferry ride from the CBD will take you to Cockatoo Island. The island has worn many hats: a ceremonial meeting place for Aboriginal inhabitants; a penal colony; a reform school; and a Royal Navy Dockyard. Explore the island's rich history with one of several guided tours.

Bondi Beach and Sydney are practically synonymous. This 1.2km stretch of sand is flanked by ocean pools – Wally Weekes to the north and Icebergs Club to the south. For a bird’s-eye view, take the coastal walk from Bondi to Bronte – or continue on to Coogee for more stunning views.

Visit Sydney’s Taronga Zoo to meet Australia’s unique wildlife: the zoo is home to more than 4,000 creatures. Adrenaline junkie activities include a zip line and elevated rope course, or slow down with a stay at the on-site eco resort and wake up to breakfast with koalas.

If you’re more into flora than fauna, head to the Royal Botanical Garden. This richly biodiverse oasis is home to more than a million species of plants and a packed calendar of events. Enjoy a guided tour, embark on a nature therapy walk or learn more about Aboriginal culture.

Many who travel to Sydney also take the two hour train ride to Katoomba, trading seascapes for mountains. Blue Mountains National Park takes its name from the blue haze caused by eucalyptus trees. Hop onto the Scenic World cable car and glide by the famed Three Sisters rock formation.