Getting around Sydney by rail or bus is simple and good value; taxis supplement the services, and are frequent, especially at night when you are most likely to use them.
There is a monorail that operates between the city centre and Darling Harbour, and this has some good views.
A great way of seeing the sights of Sydney is to get on one of the many ferries that operate around the harbour. The one to Manly is the best - because you get a nice destination to explore at the far end.
Driving in central Sydney is slightly less fun than driving in Central London, and should really be avoided, although if you are planning on getting out of the city at all, it pays to hire a car for longer trips, and theis can be easily arranged prior to travel.