My question is with really only weekends to spare and pretty new to the sport and Melbourne, how much access to the flat stuff or surfy stuff am I likely to get.
Welcome Northern Monkey, I'll look forward to seeing you out and about. You could get out every weekend in Melbourne if the last few months are a guide. Access to the bay and surf depend where you live. From Melbourne it's about 10-15 mins to the bay and about 1.5 hours to the surf. Every so often we head out for a night paddle down the yarra which is kind of fun.
As for buying one you should see if you can demo a few first first and look around, no need to worry about getting a board across the Nullabor then.