Take a walk from Bondi to Maroubra Beach. Around 5-6 km I think but it will be worthwhile. Drop by La Perouse during sunset..the place is magical. Buy that three tickets offer (Sydney tower, Zoo and Aquarium I think). Opera House and take the ferry around it. Kings Cross if you want nightlife. Blue mountain if you like outback and physical activity. Visit the universities for pretty buildings. Whale watching etc