Park At Tallarook, Train To The City
Why not take the hassle out of driving in Melbourne, park your car on the edge of the city, throw your gear in a small bag, strap it to your bike and jump on a train. If you have read my post on great rail trails on the Hume highway M31, you will realise that Tallarook is great little place to stop for a ride. It is also a great place to leave your car for a night and catch a train into the city.
When you get to Southern Cross, walk your bike to the south bank of the Yarra river and you are on one of the great inner city track networks in the world. You can ride for an hour down the Yarra or up Gardiners creek and probably to many other places.
Melbourne has great trails and they are not on roads.
Notes: You will need a Miki Card for Melbourne trains and if you don't have one, probably better to stop in Seymour and purchase a paper ticket. Any further out than Seymour and you will need to read the bike rules for the country trains carefully. Best if you don't travel at peak times before 9:30, the vic rail website may help on that. As a general rule if its a city train, getting your bike on the train will be easier. But I have only done it once. Here are some photos of my ride from South Bank up Gardiners Creek via the Yarra. I rode for an hour and never went on a single road so do you really need a car.