The Taronga Zoo can be reached via ferry. Your admission price allows you to ride the gondola up to the zoo entrance. Starting at the top of the zoo, you essentially walk down the hill and end back at the ferry terminal.
If you won't be getting out in the wild while visiting Australia, this zoo is a must. You can see all the native animals here: wombats, echidnas, kangaroos, wallabies, and koalas. They also had some animals I'd never seen at zoos before: tafirs, meercats, and tahrs.
They are building an Asian animal pavilion, which was unfinished when I was there.