I train in Bendigo (Aikikai), but we regularly trek to Melbourne for training at the head dojo in Clifton Hill. Aikikai has a large number of dojo in Melbourne. The site is http://www.aikido.org.au
Another large style with a number of dojo is Field Aikido (Iwama). My brother and sister-in-law train in their dojo.
There are a number of others out there. I would suggest getting on the mat with a few different styles and see what suits you best.
I started with Aikikai as it suited my tastes and requirements after 20 years of karate, but I've found its very personal.
I suppose one handy feature of Aikikai in Melbourne is there are a number of 40+ year practitioners. The styles vary of course, but you can't beat learning from someone with lots of years under their belt