Watson's Bay is at the peak of the South Head of Sydney Harbour. It is a beautiful, peaceful suburb with plenty of things to see and do. On the coastal side, the main attraction is the walk around The Gap. The rockface along here is spectacular - sandstone crevaces dropping anywhere from 30-60 metres into the ocean below.
You can continue walking along this path all the way to the lighthouse on the Head.
On the harbour side, Watsons Bay is a very scenic beach front, with a number of great fish and chip shops (Doyles, which is an exclusive Sydney fish restuarant, runs a 'take-away' shop here that is high quality and very reasonably priced), as well as the Watsons Bay hotel, a predominantly open air pub, that serves great seafood lunches looking across the harbour toward the city.
Getting to Watsons Bay is very easy by ferry from Circular Quay, or by bus - catch the 324 or 325, or the L24 or L82 (faster) from Circular Quay.