I'm training at Lilydale out in the east - good flying school, two grass strips, not a lot of traffic so you don't spend a lot of time waiting on the ground. Piper Warriors, Archers, and Jabirus. May be a good option if you're unfamiliar with Oz airspace.
Other main airport is Moorabbin - busy towered GA airport, several flying schools, closer to city than Lilydale.
Lilydale Airport
Moorabbin Airport - Melbourne Australia.