Oh, and another suggestion. Rather than hiring a car, you might want to consider a car share company like GoGet or Flexicar. Reasons being a) parking in the inner suburbs is a right pain in the bum, and b) a lot of things you might want to do in Melbourne are better accessed via tram and bus anyway (and you’ll want to do some tram riding. Trams are cool! Can’t go to Melbourne and not get on a tram)
If you want to do a socio-demographic tour of Melbourne, then you can cruise the streets of Toorak, Caulfield and Hawthorn for some magnificent examples of how the aristocracy live. Victorian and Georgian mansions abound, and they’re pretty sweet. Ripponlea and Como House are both open to the public (IIRC every day) and definitely a visit into another world.
For the flip side, you can drive through Heidelberg, Preston and parts of Frankston (which is where I live!!) We make do with brick veneers circa 1960. Alas, no history, but lots of crime and social dysfunction. We’re more colourful than those posh suburbs but. 