I love watching birds - I'm lucky enough to live in an area with enough trees to hear little chirps and tweets, and the raucous squawks of the lorikeets in the afternoons! There's also flying foxes that hang out in the berry trees near Stanmore station at night, you can get quite close to them and see them really well.
I've also spotted a few ringtail possums around the grounds of Sydney Uni, scavenging for food after everyone's gone home for the day. So cute!
The CBD and Inner West, however, aren't the greatest spots to see wild animals.
If you want to see and hear a huge range of birds, and maybe if you're lucky some tiny marsupials, head to the Blue Mountains and go on a hike along any of the gorgeous trails. You could get lucky and see some wallabies!
I've also heard that the Manly ferry can be a good start to spot whales and dolphins, as they don't come close enough to the main Sydney Harbour for you to see them from any of the other ferries.
Unfortunately, there's little to no wildlife in my area, we've only got pigeons, cats and the occasional bat. So when I want to see local wildlife, I go to the Sydney Wildlife Park in Darling Harbour. It's got amazing exhibits, with mammals, birds, insects and reptiles. Some of the standouts are the kangaroo exhibit, where you're just an arms length away from the surprisingly big animals, and the butterfly room where beautiful butterflies might land you if you're still enough!
Living on the fringe of the great urban sprawl that is Sydney, in that shadow of the Blue Mountains, at Glenmore Park, I am blessed with being able to see a variety of wildlife in my own yard. We are often visited by native finches, rosellas, grass parrots, sparrows and dozens of other kinds of birds. I even spotted a blue tongue lizard in my vegie patch. After a short car ride to Orchard Hills I can even see kangaroos enjoying the grass romping on land owned by the military. On occasion I have seen frogs and native mantids,
I found the Sydney Walkabout Wildlife Park in Calga to be an amazing opportunity for seeing wildlife. Not only can you see the animals up close as you walk amongst, some you can even pet! It was at this wildlife park that I petted my first ever kangaroo. However, the park focuses on Australian Wildlife, so do not expect to see as many animals as you would in a place like Taronga or Dubbo Zoo.