If you only have time for one thing to do while in Sydney, then a walk around the harbor area is the way to go. There is so much activity in the area that you really don’t need to do any planning: You have photos ops like the bridge and opera house, shopping in The Rocks, tons of pubs and restaurants and a variety of street performers.
A walk from Dawes Point Park (basically under the Sydney Harbour Bridge) to the Sydney Opera House will probably take you a few hours, because you’ll just end up stopping and taking in the culture. A great way to spend a day – and if the day isn’t over, you can keep on walking through the Botanic Gardens and up to Hyde Park. The walk by itself is free – you decide how much money you want to spend along the way.