As a regular visitor to Sydney from Interstate, a visit to both Watson's Bay and Manly by ferry are musts. When I arrive at Watson's Bay by ferry I go on a walk to the left along a small beach and interesting residential area to the Harbour overlooking the Entrance. Then I return and have a seafood lunch at Doyles on the jetty. Then I walk through the park to The Gap on the Oceanfront and walk along the clifftop until I've had enough. Then I catch the local bus to North Bondi, where I have a drink at the RSL with its beautiful view along Bondi Beach. Then I walk along Bondi Beach to Icebreakers where I watch the swimmers in the rock pool, plus on Bondi Beach, You can continue to walk along the waterfront before catching a bus back in to the city.
Manly, I do as others have suggested, except there is a lovely harbour front walk to the left as far as the Spit Bridge as well.