Circular Quay, Opera House, Botanic gardens, another shout for the bats, you get very close to them. The Rocks market is pretty good if you are there on a Sunday. Feery from Circular Quay to Darling Harbour to get great view of Bridge from the water. take ferry to Watsons bay and visit The Gap, great views from there back to downtown, and a great Restaurant is Doyle’s on the beach.
Bondi is a litte overrated, but worh seeing, take bus there then walk to Coogee along the cliff walk and bus back from there.
I did enjoy Taronga zoo, but its a zoo….. better exploring other places – train to Katoomba for Blue Mountains, very do-able in a day.
I never tired of the Bridge/Opera house view and the walk along from Circulay Quay.