The best way to explore Sydney is by ferry. This a cheap opportunity to cruise the spectacular Port Jackson, Sydney's natural harbour.
Another good way to get around Sydney is to get a combined Rail/Bus/Ferry pass so you can try out a variety of transportations.
I really recommend the Ferry. It's very nice out on the harbour.
Ferries are by far the best way to get around. Really nice relaxing way to travel and you get to see the best bits of Sydney. Regular schedules and convenient destinations.
It is a 12 minute ferry ride from Circular Quay. And the journey offer passengers an off-shore view of Opera House.
Take the Ferry system for a cheap tour of the harbor. The ride back from the Toonga Zoo takes you to a few really neat parts of the harbor.