I studied in Frankston, outskirt of Melbourne (abt 1 hr away) and i can say the public transport is quite good.
In Melbourne, u have the free tram around the edge of the city. Most people also take the paying tram or trains as well as buses. Most of the time, it's not too crowded and come at regular intervals. From a tourist point of view, it is good enough to bring you to many places. However, if you want to go to some places liek Great Ocean Road etc, your probably ahve to drive or take a day tour.
it's convenient for me ...
it really depends of the nature of travel itself. for everyday commuting between places, it's good enough.
for holiday..it's best to rent a car so you can explore more places that are not covered by public transport. and most good places don't have public transport..hehe.