I've heard wonderful things about the Taronga Zoo in Sydney, however when we arrived I asked someone for a less commercial zoo, looking more for a sanctuary where the animals are a bit more free to be themselves.
We took the 40 minute train from downtown Sydney and walked around Featherdale Wildlife Park.
We got to hand feed kangaroos, wallabies, and koala bears. These animals were all very friendly and always up for a photo!
Various bird species are in the park as well.
I highly recommend this train ride for a day or even half day if you're crunched for time. The animals are quite impressive.