If you are looking at national parks/leafy suburbs etc come over East way. Grabbing a rental in Box Hill is a good idea to start with. I'm at the foot of the Dandenong Ranges, close to national parks, the lovely hills, childrens farms, arboretums.
It's all very established out here and you should be able to find something lovely with a big backyard within that price range.

Look at Heathmont, Boronia, Ferntree Gully, The Basin, Wantirna - they are about 10-15 mins from Box Hill.