Ferry ride to Cockatoo Island. Easiest is to catch the ferry from Balmain Wharf, you can buy a ferry ticket onboard.
Cockatoo Island has a lot of history. There are plaques to read all over the island! (but not so many cockatoos anymore...)
These days it is home to many events, especially Underbelly Arts Festival and The Sydney Bienalle.
In this tunnel hidden is fun.
You will need the number 121. (And a half.)