Loads to see in Sydney. Public Transport is very good.
The Opera House. The Rocks, The Bridge Climb, Walking in The Botanical Gardens, The Aquarium in Darling Harbour, take a harbour cruise, Taronga Zoo (take a ferry ride there) The shops(especially the Queen Victoria Bldg) The cafés and restaurants. Bondi Beach though I preferred Manly Beach, The Blue Mountains you can get a train out there or take a tour, and loads more.

A good guide book is the AA City Pack on Sydney. It has a good map and loads of info about what to see so that you can plan your sightseeing before arrival.

Ferry to Manly.

I loved the afternoon tea cruise on the Bounty around the harbour. It's the actual ship that was in the film.

luci

Defo head to Manly, the best beach going, and go round to freshwater beach, the first place surfed in Australia. Go to the northen beaches of Avalon and Newport (Home and Away films there ) Train up to Blue Mountains and maybe onwards to Bathurst. South to Bundeena by Cronula for the National Park some amazing cliff walks. Oxford Street and Paddington worth strolling around. Buses and trains are fantastic. There are a lot of discount tickets available too, so you can save money.

Want to swap places.......

Hi
You have been given good advice so far a trip up the Centre Tower in Pitt street gives good views of the city.
To go to the Blue Mountains take one of the one tours that go up there much better than being let of at a railway station and having to find your way around