I love Autumn. Not only for the Autumn leaves, but also Autumn means its mushroom hunting time!
Before you go mushroom hunting though make sure you know how to recognise the difference between edible and inedible mushrooms. The 2 most common edible mushrooms I've come across in my ramblings are Slippery Jacks and Saffron Milk Caps (i.e. pine mushrooms). Both are very distinctive and a quick google search will tell you how to recognise them.
Just remember - if you're in doubt - go without!
In terms of where to find edible mushrooms in Melbourne, there are numerous places but generally anywhere you can find pine trees will yield these edible mushrooms. Places you may wish to try: