Sydney's climate is at its most forgiving during spring – October is the month with the lowest rainfall and average daytime temperatures are a balmy 22C.
Sculpture by the Sea (sculpturebythesea.com; 24 October-10 November) is a collection of sculptures along the Coogee-to-Bondi coastal path.
Or you could celebrate the 40th birthday of the Opera House at a special concert on 27 October, featuring the Sydney Symphony Orchestra, Opera Australia and Sydney Philharmonia Choirs; tickets are available from A$40 (£25) (sydneyoperahouse.com).
Get your bearings
The Sydney Harbour Bridge links the north and south sides of the city, with the Circular Quay ferry wharves and the Opera House located just east of the southern bridge pylon.
This is also the location of the "CBD" (Central Business District), the main features of which are a procession of clothes and luxury goods stores – and the glorious green spaces of Hyde Park and the Botanic Gardens. Before you do anything else, though, pop into The Rocks Visitor Centre at the corner of Argyle and Playfair streets (sydney.com; 9.30am-5.30pm daily).
The City Circle rail line provides handy links between the Central Station, Town Hall and Circular Quay. Buy tickets at rail stations, ferry wharves and on buses. Best value is the MyMulti DayPass – A$22 (£14) to use the transport network including ferries.
Take a view
If your accommodation doesn't come with a view of the bridge, head to Sydney Tower Eye, atop the Westfield building at the corner of Pitt and Market streets. At 309 metres this is the city's tallest building; the 360-degree view reveals how far the harbour extends both east and west, and there's the option to try the giddying open-air Skywalk (sydney towereye.com.au). Booking in advance saves 30 per cent on the A$26 (£16) walk-up price. Open daily 9am-10.30pm.
Take a hike
The six-kilometre cliff-top path that links Coogee Bay with Bondi Beach (take the 372 or 373 bus from Circular Quay to Coogee and start by the north end of the beach) is the most popular walking trail in Sydney. You pass two other surf beaches (Bronte and Tamarama) and two narrow coves (Gordon's Bay and Clovelly). There are drinking fountains along the way, so just bring a towel for a (slightly chilly) swim on a warm spring day.
Steep sets of stairs mean this route is not wheelchair accessible, but the same path south from Coogee has no stairs; following this route for half a mile affords its own stellar views of the cliffs towards Bondi. See bonditocoogee walk.com.au.
Lunch on the run
The Bucket List on Bondi Beach (thebucketlistbondi.com), is just the place to land after you've tackled the Coogee-Bondi path. It's all nice and obvious: grilled fish, fish'n'chips, pinot gris and riesling. Expect to pay A$19 (£12) for a John Dory fish-burger.
Located halfway between Bondi and the city, Paddington's The Intersection is a side-by-side collection of clothing stores that represent some of Australia's most renowned new fashion designers. The likes of Ellery Boutique (elleryland.com), Ginger & Smart (gingerandsmart.com) and Zimmerman (zimmermannwear.com) can be found at 16 Glenmore Road, Paddington. Stores are open daily.
Dining with the locals
Café Sydney in Customs House, 31 Alfred Street (cafesydney.com) is right beside the harbour and has an outstanding roster of wines and cocktails to go with expensive mod-Oz cuisine. A main course of Cone Bay barramundi costs A$39 (£24). A cheap-and-cheerful dining option is Frankie's Pizza, which opened last year at 50 Hunter Street (frankiespizzabytheslice.com). The place is packed day and night, serving traditional pizza pies and pizza by the slice (A$5/£3).
Out to brunch
That Sydney's great brunch tradition is "Yum Cha" (dim sum) is a reflection of the quality of the restaurants and delis that make up the Chinatown neighbourhood. Try it at Marigold in the Citymark Building at 683 George Street (marigold.com.au) but book well ahead for weekends. The Yum Cha degustation menu costs A$30 (£19) per person.
A walk in the park
The Royal Botanic Gardens are small enough to mean that you're never far from the harbour and also have interesting wildlife, including flocks of white sulphur-crested cockatoos (rbgsyd.nsw.gov.au). Open daily. It's less than a mile from the gardens to Hyde Park, where possums bound around at dusk as if they own the place.
Go to church
On College Street, St Mary's cathedral is the seat of the Archbishop of Sydney. Here a statue of Mary MacKillop – who in the 19th century established an order to educate Australia's rural poor and who in 2010 became the first and only Australian to be canonised a saint – can be found on the city side of the building (stmaryscathedral.org.au). Mass times vary (see website); open to visitors daily.
Take a ride
Every guidebook lists riding the Manly ferry as Sydney's must-do day trip, but an alternative with a bit more muscle is rumbling around on the back of a Harley-Davidson.
Blue Thunder Downunder (bluethunderdownunder.com.au) will pick you up for a one-hour tour of harbour bays and beaches. One bike plus guide (who drives it with you as passenger) for one hour costs A$130 (£81).
The Museum of Contemporary Art, or MCA, at 140 George Street (mca.com.au) features everything from works by Chinese dissidents to Aboriginal artists who present alternative views of colonial Australia through painting, photography or film. Open daily, entry free.
Icing on the cake
Since its launch in 1998, Bridgeclimb (bridgeclimb.com) has led almost three million people – the majority of them foreign tourists – up the 1,439 steps of the south arch of Sydney Harbour Bridge for an unobstructed view of the harbour. Groups have a maximum of 14 people and the climb takes three-and-a-half hours. Ticket prices vary according to the time of day, from A$198 (£124) to A$308 (£192).