Redleaf Pool and Nielsen Pool
Sydney has a number of wonderful, completely free, public "pools". They generally constitute some netting to keep out larger fish (read sharks), a sandy beach, a snack shop and good fun.
Redleaf Pool is one of the closers ones to the Sydney CBD. Step off the bus on New South Head in Double Bay, walk down some steps and it's right there. It's a giddy mix of young and old enjoying all that Sydney has to offer. The views of Double Bay and the harbor are lovely as well.
The enclosure for Redleaf Pool actually has a walkway where you can take a stroll over the water or jump in. At high tide, the water comes right up to the walkway so it's just a short jump into the water. At low tide, it's much further down, adding a sense of adventure to the experience. Two rafts float in the middle and provide a place to sun yourself before swimming back in.
Nielsen Pool aka Shark Bay
Nielsen Pool, also know as Shark Bay, is a little further from the CBD in posh Vaucluse. And instead of being right on a busy throughfare like Redleaf Pool, it's set inside leafy Nielsen Park. The views here are less urban and more green. There's a small playground and a nice walk along the water that heads back to Rose Bay.