Taronga Zoo is a lot of fun for kids and adults. We saw all the usual zoo animals--elephants, lions, chimps, reptiles, bears, seals, penguins, etc.--as well as local Australian animals like kangaroos, wallabies, koalas, dingos, echidnas, Tasmanian devils, wombats, emus, etc.
The best part of Taronga is the view. It's set up on a hill with fantastic views of Sydney Harbour, the Opera House, and the Bridge. It's accessible by ferry from Circular Quay, then a short cable-car ride up to the zoo entrance.
Get there early if you want to get your picture taken with a koala.