1: BridgeClimb There's no better way to start a visit to Sydney than by climbing the Harbour Bridge. Four-year-old operation BridgeClimb has taken nearly a million people up to the 134m-high summit of 'the Coat Hanger', as it's known by Sydneysiders. The whole experience takes three-and-a-half hours, from being kitted out in grey jumpsuits to picking up your certificate and souvenir photos at the end. It's entirely safe - each climber wears a belt that is secured to a safety railing at all times - though the organisers warn, with some understatement, that if you suffer from vertigo or fear heights it 'may impact on your ability to participate'. As you climb above the trains and traffic that thunder across the bridge, you'll pass some of the six million rivets that hold the structure together. Before you know it you are at the top, being buffeted by the wind and admiring a view that stretches from Bondi Beach to the Blue Mountains, 50km away. The climb costs A$145 (HK$640) per person. For bookings call BridgeClimb on  8274 7777 ( www.bridgeclimb.com ). 2: Fort Denison One of the harbour islands you'll have seen from the bridge is Fort Denison, which was known to local Aborigines as Mat-te-wan-ye. During Sydney's earliest years as a penal settlement, the British turned it into a prison within a prison, marooning the most recalcitrant convicts on a meagre diet of bread and water - hence its earlier name, Pinchgut Island. It was later turned into a fortification and boasts one of the best preserved Martello towers in the world. It's looked after by the National Parks and Wildlife Service (NPWS) and is one of the best places in Sydney for breakfast - an early morning ferry runs from Circular Quay three times a week. Breakfast tours run on Tuesdays, Thursdays and Saturdays. A$37 per person. Bookings essential. Call NPWS on  9247 5033 ( www.npws.nsw.gov.au ). 3: Woolloomooloo The harbourside district of Woolloomooloo is compact and full of attractions. Start off with a swim in the newly refurbished Andrew 'Boy' Charlton outdoor swimming pool, named after an Australian swimming champion of the 1920s. A sleek concoction of glass and steel, the pool sits opposite the Garden Island naval base, looking directly across to the destroyers and frigates of the Royal Australian Navy. After cooling off with a dip (beware the 'pool Nazis' who relentlessly plough up and down the marked lanes), head round the bay to the Finger Wharf, a restored cargo wharf built on the eve of World War I, which is now home to the luxurious W Hotel (tel:  9331 9000; www.starwood.com/whotels ). Inside its cavernous foyer, which features original wooden conveyor belts and giant rusty cogs, you'll find the lounge-style Water Bar, a good spot for a pre-dinner sharpener. A couple of minutes round the corner lies Otto's Ristorante Italiano, one of Sydney's legendary eateries. A favourite hang-out of the rich and famous, the restaurant looks out on to a marina, and beyond that to the city skyline (tel:  9368 7488; www.ottoristorante.com.au ). 4: Bondi To Coogee If all that eating and drinking has left you feeling a little out of shape, head for the coast for one of Sydney's finest attractions - the cliff-top walk from Bondi to Coogee. Kick off the walk with a coffee at one of Bondi's many pavement cafes, then pick up the coastal path and meander slowly south to Tamarama, nicknamed 'Glamourama' for its popularity with Sydney's beautiful people. The next beach along, Bronte, has crashing waves and a strip of restaurants that make it a great lunch stop. The eatery, Sejuiced, offers thick berry shakes and ciabatta sandwiches, while a few paces along you'll find the Bronte Chippa, which serves takeaway fish and chips. From there you'll walk through a surreal but strangely beautiful cemetery before dipping down to Clovelly, a narrow bay which is popular with snorkellers. Look out for dolphins and, from May to October, humpback whales as they migrate from Antarctica to Queensland. Another kilometre on from Clovelly brings you to the rowdy backpacker pubs and crescent-shaped beach of Coogee, where you can catch a bus back to town. 5: Let's Go Surfing After watching the local waxheads carve up Bondi's pounding surf, you may feel like trying it yourself. Grab a towel and head for Let's Go Surfing, a local firm that operates from a hole-in-the-wall shopfront at the north end of Bondi Beach. First-timers are welcome, and are shown the basic techniques - paddling while lying on your stomach, leaping into the crouch position - on the beach. Then it's time to get in the water and put the theory into practice. Catching a wave is harder than it looks, although Let's Go Surfing's instructors say most people are able to stand up - if only for a matter of seconds - during their first lesson. A two-hour surf lesson costs A$49 per person. Courses 365 days a year (tel:  9365 1800, www.letsgosurfing.com.au ). 6: Horizons Bar Sydney has countless great watering holes but Horizons cocktail bar offers perhaps the finest views of the city, especially at night. Located on the 36th floor of the ANA Hotel in the historic Rocks area, it overlooks the Harbour Bridge, the Opera House and just about everything else of interest. Head up there at dusk, when the sunset paints the western sky with streaks of pink, blue and gold. As well as all the classic cocktails, you might want to try the Spirit of Sydney, a potent mixture of butterscotch schnapps, banana liqueur, chocolate liqueur, and orange and guava juice. Cocktails start from A$16 (ANA Harbour Grand Hotel, 176 Cumberland Street, The Rocks. Tel:  9250 6013; www.anahotelsyd.com.au ). 7: Sydney Harbour Kayaks For a city of four million people, Sydney has some amazingly unspoilt beaches and coves, and the best way to experience them is by kayak. Sydney Harbour Kayaks operates from Manly, a 30-minute ferry ride from Circular Quay, where guides will take you into some of the quieter backwaters of Middle Harbour, a branch of the main harbour. Paddle past the evocatively named Forty Baskets Beach and on to Reef Beach, a haunt for local nudists. Long stretches of untouched bushland are interrupted by some of the city's most expensive real estate - luxury homes that tumble right down to the water's edge. Most trips take in the mangrove-lined creeks of Bantry Bay before ending at The Spit Bridge, a marina and beach area from where there are regular buses back to the city centre. Half-day excursions start from A$69 per person (tel:  9960 4389; www.4shk.com ). 8: Sydney Harbour Seaplanes If paddling your own kayak is a little too strenuous, another great way to see the harbour is to take an old-fashioned seaplane from Rose Bay to the Hawkesbury River, an area of creeks, bays and wooded bluffs to the north of the city. There's something raffish and very 1930s about the little De Havilland Beaver float planes, and you half expect your pilot to be wearing a leather flying jacket and a pair of goggles. The 15-minute flight takes you across the harbour and along Sydney's spectacular northern beaches, including Dee Why, Curl Curl and Avalon, before touching down either at Palm Beach, home to the seriously rich, or at one of two riverside restaurants further north: Peats Bite and The Cottage Point Inn. The latter sits beside the tranquil waters of Cowan Creek and has a private wharf. Flights, including lunch, cost A$335 per person (tel:  9388 1978; www.sydneyseaplane.com.au ). 9: Centennial Park After the seaplane experience, you may well be looking for a couple of hours' entertainment that won't break the bank. Centennial Park is one of the city's most popular green lungs - the perfect place for a stroll in the sunshine and a picnic beneath giant Moreton Bay fig trees. Its smooth bitumen perimeter road is ideal for rollerblading. As you whizz along beside cyclists and fit young mums running behind baby joggers, you can even do a spot of birdwatching: the park's lakes and wooded thickets are home to pelicans, ibises and flocks of screeching black cockatoos. After a couple of laps on your blades, there are plenty of cafes in nearby Paddington and Darlinghurst to provide a restorative coffee or lunch. You can hire rollerblades outside the park at Total Skate (36 Oxford Street, Woollahra (tel:  9380 6356; www.totalskate.com.au ). 10: Paddington No trip to Sydney is complete without some retail therapy, and Paddington's Oxford Street is the place to start. Aside from the ever-popular Paddington Markets, which are open every Saturday, the street is crammed with boutiques and clothes shops, from Lisa Ho to more mainstream outfits like Esprit. If you need to wet your whistle, have a drink at the light and airy Paddington Inn or the art-deco Light Brigade just up the road. Chocoholics will want to skip the beer and head straight for The Chocolate Bar. In addition to glass shelves loaded with hand-made chocolates and delicious brownies, try its speciality, the Suckao. A waitress will give you a white porcelain bowl filled with milk, which rests on a tiny candle. As the milk heats you drop in tiny shards of chocolate and wait for them to melt. Not to be missed (447 Oxford Street, Paddington. Tel:  9357 5055).