If you have some spare hours, take a walk from Bondi Beach to Coogee. You'll walk past some great beaches: Tamarama, Bronte and Clovelly; all smaller and less crowded than Bondi.
The mysterious rock at Ben Buckler Point (the point in North bondi) is said to have been washed up by a storm in 1912 - it weighs over 200 tons! Take a look at it! :) And while you're there, walk round Ben Buckler, you'll get a great view and photo opportunity of the beach!
In the middle of August every year there is a Fun Run from the city to Bondi Beach. Even if you don't join there's lots of people and partiies all evening in Bondi! This year the winner was actually a Finish traveller! :)