Where I live the local polling booth is around 200m from my house. A gentle stroll, and there you are. Alas, very little usually on the cake and sausage sizzle front though. And apparently voting for local government here isn't compulsory either.
Re not seeing the critters - lots of our natives are nocturnal, so they'll be curled up in burrows or hollow trees or branches all day. The only time I've seen a possum out in daylight hours was in FN Queensland, and it was a blind one.
I've only seen two or three wallabies here (Tasmania) during daylight hours, but at night... wow. One night a few months ago I counted 27 in a 15km stretch of road. Poor things were crossing to get to the river on the other side, and there was a bush fire up in the hills behind them. Pademelons come out in shadier forested areas sometimes, if you want a native animal to squee over, these are it. Tiny little fat kangaroo-like things, about half the size of the average house cat. If you're very quiet and still, they'll come right up to you. http://www.flickr.com/photos/ron-alenka/2048205518/
I've seen one wild wombat, at night right next to the road. They look so much like rocks sometimes, it's hard to tell. I do see a few echidnas about, they're adorable things. The Tassie ones tend to be more furry and less prickly than the mainland ones. And you can still occasionally see platypus in the local rivers on overcast days.
We also get flocks of yellow-tailed black cockatoos here - they sit in the top of my pine trees and rob the cones. Noisy as heck, but they're spectacular in flight. Flocks of sulphur crested cockies and pink and grey galahs are common, and in the rural areas I often see other small parrots such as green lorrikeets feeding on grass seed.
The best place to see Tasmanian Devils now, unfortunately, is in one of the wildlife parks. The facial tumour disease has really knocked the population badly - they estimate around 90% of wild devils have been affected and died. It's tragic. Devils are gorgeous, awkward, dopey looking things about the size of a small dog - they sort of wander around, blinking a lot at the light, staggering slightly as if they're drunk. They can open their mouths incredibly wide, and they really do turn into Taz at feeding time!http://tasmanpeninsula.com.au/wp/attractions/tasmanian-devil/http://www.animalpictureplace.com/tasmanian-devil-pictures/tasmanian-devil-growling.jpg.php