5. Tour the Opera House and cross the gardens for a ’loo stop.
This is doable on foot but you may want to get a ride back. Swap the Botanic Gardens for the Domain, and you can bike it. From the Opera House – the basic tour is a reasonable $23 - head south into the gardens to gawk at the gothic pile of Government House. Entry is free, or you can just relax in the English-style garden. Then join the army of joggers and walkers along historic Farm Cove. You can criss-cross through the Botanic Gardens, maybe taking in the Herb, Rose and Succulent Gardens, or continue along the harbour to Mrs Macquarie’s Point with her eponymous chair, the best seat in Sydney. Head back south along Woolloomooloo Bay and you’ll sight another of Sydney’s famous pools, the Andrew (Boy) Charlton Pool, right on the bay. Follow Cowper Wharf Road past the redeveloped Finger Wharf and its airy apartments and al fresco cafes. Once the domain of wharfies, it’s now home to Russell Crowe, among other glitterati. Fuel up with a mushy-pea pie from Harry’s Café de Wheels, a Sydney institution since 1945. Head up the McElhone Stairs to Potts Point and Kings Cross, if you have the energy, or head back toward the city, stopping in at the Art Gallery of NSW. Entry to the excellent permanent collection is free.

6. Mingle with the multicultural mob in Bondi
Australia’s most iconic beach is so endlessly filmed and photographed that even first-time visitors are swamped by a wave of déjà vu. Yet Bondi is a must-do. Ironically of course, in this quintessential Orstralian setting, you’re as just as likely to bump into Russian residents and Japanese tourists as you are bronzed lifesavers and surf-loving supermodels. If the scene on the crowded sand runs out of interest, head out on the cliff-top walk (mind the jostling – every other jogger seems to be a triathlete-in-training), past yet another iconic pool, the Icebergs Club. The next beach you come to, set in a small deep bowl, is Tamarama (aka “Glamarama” on account of the photogenic qualities of the sunbaking set). You can continue on to Bronte Beach and all the way to Coogee Beach, a couple of hours away. Bondi’s funky market sets up on Campbell Parade on Sundays, but for personal and mental space, better to do the walk on a weekday.

7. Ogle the passing parade at Paddington Market and Oxford St
The Saturday market around the Uniting Church, on the corner of Oxford and Newcombe streets, is an essential Sydney experience, with fab vintage, high-end craft, homewares and out-there designs among the merchandise. It’s a crush of colour, with the high-maintenance people and poodles not least of the attractions. For more elbow room, take a seat at a café in Oxford Street, the loud and proud hub of Sydney’s gay community. The Mardi Gras takes place in late February/early March, but you can enjoy the passing parade here any time of the day or night.

8. Cruise Vaucluse
For blue-chip Sydney real estate, Vaucluse is about as desirable as it gets. If Double Bay is dubbed Double Pay, Vaucluse, in the exclusive east, is double pay with a very generous bonus and stock options. Its few winding streets, totally tailored to the view, mean you can cruise or easily walk around to take in the gob-smacking residences, which range from historic mansions to modern masterpieces worthy of Architectural Digest covers. But you don’t need to own to enjoy the best views. Take Vaucluse Road to Nielsen Park and wander down to Shark Beach (so called because of its shark nets). This is a great kiddies’ swimming spot and arguably the prettiest beach on the harbour. Nielsen Park Kiosk, overlooking the water, is a great spot for lunch. Around Vaucluse Point to the east, overlooking narrow Vaucluse Bay, is the turreted Vaucluse House, built in 1803 and still surrounded by ten sweeping hectares of gardens and grounds. A tour costs $7, or you can put that toward tea and scones at the Tearooms.

9. Watch the sun set from Watson’s Bay
Serving up seafood and superb views, Doyle’s at Watson’s Bay is probably Sydney’s most famous restaurant. For those who like their fish ’n’ chips on paper, not plate, there’s a takeaway window. Walk off some of the grease with a trek up to South Head and the postcard-pretty Camp Cove. The last beach before South Head is the nudie Lady Jane. On the ocean side, The Gap Park has (yet again) heroic views. Finish back at Watson’s Bay to watch the sun set over the Harbour Bridge before hopping on a ferry back to Circular Quay.

10. Plod through Paddy’s Markets, then chow down in Chinatown
Paddy’s Markets (not to be confused with Paddington Market), housed in a massive red-brick barn on Hay Street, has been going since 1834. Open Thursday to Sunday, it’s vast rather than interesting but a convenient stop for cheap traveller essentials. Chinatown, at the south-west corner of the CBD, centred on Dixon St (just across the road from Paddy’s), ticks the boxes for colour, bustle, tantalising sights and smells, and choice of chow palaces. You can spend what you like on exotic fare – sea cucumber and abalone, for instance - but if you can’t get a great cheap meal here, you’re not even trying.