We used to sail out of Hobson Bay YC, lovely friendly club, but that was about 20 years ago now, not sure what it is like now, or if it is still there.. (Just checked, yep, still appears to be there.)
I second the view that Western Port is worth considering. I am a Melbourne boy and sailed both on Port Phillip and Western Port from the age of four till I left Melbourne at the age of 35. Western Port was always a lot more fun.
Then, of course, there is Geelong and Corio Bay, which is the best bit of the Port Phillip waterway overall I feel, and closer to the Rip and lovely Tassie.
But of course the thing that is going to matter most is where you end up living in Melbourne. Clearly if you end up in the West, then (ironically, given the name) Western Port will be no good to you. Likewise if you end up in the South East, Hobsons Bay YC and Corio Bay will be no good either. No point owning a boat
if it takes too long to get to it and you never end up sailing it.