If you want to experience seeing the Australian possum, then take a walk into the Flagstaff Gardens in the evening. The furry brush tail possums are unusually tame here, and climb down the trees to greet passing visitors. You must not feed or disturb the possums, but they will come pretty close to you, hoping for food. The park itself is also a great picnic spot for lunch and is an easy running or walking spot.
309/311 William St, West Melbourne VIC 3003, Australia