Catch the Bondi Explorer bus on the beach side of Campbell Parade. The fare is $39 but you can ride all day and get on and off. You can change to the Sydney Explorer bus at Circular Quay for free, and you will go past almost every tourist thing in Sydney in just a few hours. Get off somewhere to have lunch and arvo tea. Plenty of scenic views, museums and stately homes along the way. Make a day of it.