I'm in Melbourne and my immediate reaction is that you would want to hire a car, but yes, more detail would be useful. For getting around Melbourne itself public transport is fine, but places like the Grampians or the Great Ocean Road and the Twelve Apostles (or however many are left!) are far easier if you're driving.
ETA: sorry, just saw your latest post. The Yarra Ranges is a lovely area, with lots of attractions - as well as the National Park there's Healesville Sanctuary, where you can see native Australian wildlife and feed kangaroos, and the Yarra Valley is a well known wine producing region with lots of cellar doors you can visit on a weekend. But pub transport doesn't make it easy. By 40 minutes from Melbourne, do you mean the city centre, where most of the tourist attractions are, or Lilydale or one of the other outlying suburbs? Because it takes at least an hour just to get to Lilydale on the train, so you'd need to add that to the travel time. Personally I'd either sign up for a tour - and it looks like there are a lot of different ones, some focusing on the wine and local produce, and some on the animals - or maybe plan it as an overnight trip rather than trying to do it in a day, and take your time.