ratc2009
The tower and the centre and the 'academy' are co-located, off the airport on the other side to the terminals. There is no public transport. If visiting for the day, then you will need to cab it to the entrance to the compound, and you can walk to any of those three locations from there (100m).
Melb is a tough gig without a car. If you get the job, I couldnt really see you getting by without one. It may be possible to cycle to the asa compound every day, but you would have to live nearby (say, Tullamarine) and be really committed. There are buses to the airport, but it's still a fair distance around the airport to the compound.
As for the difference between the centres- I would strongly advise you base your decision on where you want to live. Brissie and Melb are vastly different in that regard.