The Central Gardens Reserve in Merrylands is a good place to go to see Australian native animals like the emus, wallbies and several other types of flora and fauna. There's also ample collection of birds and water flows roaming in the manmade lake.
It is not so far from Sydney City too. It is also just under half an hour from our home. Whenever we have visitors from overseas, we also take them here as an alternative to the big zoos which can be chaotic and full of other tourists. If you just need to show Aussie animals then this is a better alternative as the entrance fees alone in popular zoos are just too steep especially if you have a number of guests.
So the bonus here is that,entrance is FREE!
It also has good picnic grounds and a useful lake system teeming with water fowls. In the past it had a lot of water features but these days they still manage to retain a few fountains. The manmade waterfalls are sadly not around anymore.