Ferries are some of the best ways to see Sydney.
Ferry to Watson Bay and have an early dinner at Doyles seafood restaurant and watch the sun set.
Ferry up the river to Parramatta
Wander around The Rocks an take a walk across the bridge, as someone said, the Pylon lookout is great.
Darling Harbour precinct is great for food.
Have a flutter the casino.
Ferry to Manly and walk to Shelley Beach.
Powerhouse Museum, Australian Museum, Art Gallery are all good.
Steer clear of the Museum of Contemporary Art (MCA) at the Rocks, they have really weird crap there (the only time I ive been, 20 years ago, they had on display a collection "used" feminine hygiene products and they called it art!)