Take a ferry from Circular Quay. Also check out the town of Manly and The Rocks also. If you want to treat yourself a Harbour Bridge climb. If not you can walk up the bridge pylon for much less and still get a great view over the harbour
I'd also suggest taking the ferry. On your way to Darling Harbour I'd recomend getting off at Balmain East which has great views of the harbour and the bridge. If you walk or take the bus up to Balmain you will find some great pubs and restaurants.
