Probably our all-time No 1 favourite free thing to do in Sydney is the 6km Bondi to Coogee walk along the cliffs passing through the inner-city eastern beaches. Vast Bondi Beach is beautiful in itself, but it's worth making it around to Tamarama, Bronte and Clovelly to Coogee. And if you have any energy after that, you can keep going to to Maroubra, which would take you about 3.5 hours. In the latter part of each year, the Bondi to Tamarama section of the track hosts the Sculpture by the Sea public art exhibit (see below).
To cool down after or during that walk, call into the Bronte Baths for a quick dip. One of the few free saltwater rock pools in the city, off-peak this is an absolute gem, with spectacular views back over Bronte Beach and the coastline. If the water is a little rough, it splashes up over the sides of the 30m pool, which is a novelty. It has a concreted bottom with lane markers, and there is a separated shallow area for children. And there are free hot showers.
This annual public art event — the largest annual sculpture exhibition in the world — is an absolutely massive event on the Sydney calendar. It's worth planning a trip to the city around, but be warned, tackling it on weekends can be busy. Still, it's worth a little crowd range to see dozens of interesting and creative artworks exhibited along the coastline between Bondi and Tamarama. Next year's event, its 21st, is on from October 19 to November 5.
Speaking of art, Sydney is home to two world-class galleries you can visit for free: the Art Gallery of New South Wales (the Domain) and the Museum of Contemporary Art (Circular Quay). Admission charges apply for some special exhibitions, but there are plenty of artworks and events on at each that you don't have to pay for, and the MCA has offers free daily guided tours.
This free light festival, which absolutely changes the face of the inner city come nightfall, is a must-see event. All the major buildings and structures around the city are illuminated with patterns from projections, including most spectacularly the Sydney Harbour Bridge and the sails of the Sydney Opera House. There's a mix of free and ticketed events, and it's really something the entire family can enjoy. Next year's festival is on from Friday May 26 to Saturday June 17.
One entrance to the beautiful Royal Botanic Gardens is just a five-minute walk from the Sydney Opera House but you could spend hours in here exploring one of the jewels in the city's crown. A nice walk is along the waterfront around to Mrs Macquarie's Chair (a sandstone bench made by convicts in the early 1800s for the Governor's wife to enjoy harbour views from) which will take you about a half-hour return. There are free one-hour daily guided walks exploring the gardens' heritage and plant diversity, or download a map and explore on your own.
Like Vivid, much of the annual Sydney Festival is ticketed, but there is a heck of a lot of stuff on the programme that's either free or very cheap. Two of the flagship events are Symphony Under the Stars and Mazda Opera in the Park, both free concerts in the Domain - think picnic hamper, rug and a big group of friends and family. Symphony Under the Stars, performed by the Sydney Symphony Orchestra, takes place on January 14 at 8pm, and will feature music by Adams, Mozart, Elgar and more; while Opera in the Park, performed by Opera Australia, is on January 21 from 4pm.
8. Walk across the Sydney Harbour Bridge
As far as landmarks go, it doesn't get much more iconic than the Sydney Harbour Bridge, which has a pedestrian walkway along its eastern side. You can start from either the southern side on Cumberland St in The Rocks, or the northern side at Milsons Pt. The walk itself takes less than half an hour, though you might be so gobsmacked by the views of the CBD, beautiful harbour, and equally iconic Sydney Opera House.
The ultimate free thing to do — at least Downunder beaches have not become commercial enterprises like they have in parts of Europe. There are lots and lots of incredible spots to choose from but two favourites are Camp Cove, a quick walk from the Watsons Bay ferry wharf to the east of the CBD where you can snorkel and swim in calm waters (parking fees apply); and Shark Beach at Nielsen Park, also in the east, which has lots of shady picnic spots, grassed areas, and a walking track.
Make some time to pop into Customs House at Circular Quay to see its amazing 1:500 scale model of Sydney's CBD that lies under a glass floor that you can walk on, giving a miniature bird's-eye view of the city. The model took 15 model makers three months to construct in 1998 and has recently been updated so that its 10sq m are as accurate as possible.