If you already have a car, why not drive yourselves? It's really not difficult - just needs one of the four of you to be the designated driver and go (very) easy on the cellar door tastings.

For wine tasting from Melbourne, you have three main choices - the Yarra Valley (north-east), the Mornington Peninsula (south-east) or the Bellarine Peninsula (south-west, round past Geelong). The Yarra Valley is the best known but they're all worth a visit. The Yarra Valley is a fairly easy hour or so drive from Melbourne and would be the more obvious choice. The Mornington and Bellarine peninsulas are perhaps a little further (if you're coming from Melbourne) but are still an easy day out.

As you know, there usually isn't much to actually "see" at a winery, depending on the time of year. For the Yarra Valley, we have tended to become creatures of habit, so usually start the day with coffee and a cheese tasting plate at the Yarra Valley Dairy Company, then round the corner to Domaine Chandon, which has a good self-guided tour, followed by a tasting flight ($) of their sparkling wines. Then on to TarraWarra (interesting architecture) to visit the Art Museum, followed by lunch there, or perhaps at De Bortoli or Tokar Estate or Yering Station. You could also spend some time in the afternoon at the Healesville Sanctuary, if that is of interest.

On the Mornington Peninsula, we like the (small) Tuck's Ridge - we always get the same guy in the tasting room and we always seem to end up going home with a couple of cases of their reds .... not quite sure how it happens.... :-)

You can easily research the wineries in each area online. Pick a few that you like the look of, find them on the map and off you go... A number of the wineries will give you a pretty decent lunch - perhaps worth checking out the menus online ahead of time and, depending on when you're going, probably need to make a reservation. One restaurant that has become very 'fashionable' is Ten Minutes By Tractor on the Mornington Peninsula - definitely make a reservation well in advance if you want to go there.

http://www.yvd.com.au
http://www.chandon.com
http://www.tarrawarra.com.au
http://twma.com.au
http://www.tokarestate.com.au
http://debortoliyarra.com.au
http://www.yering.com
http://www.zoo.org.au/healesville

http://tucksridge.com.au
http://www.tenminutesbytractor.com.au

As for the car, where else are you planning to go? A car in Melbourne is a bit of a liability - you don't need it to get around town (walk or take the tram), parking is expensive and you have to deal with those 'hook' turns (designed to confuse the visitors...).

https://en.wikipedia.org/wiki/Hook_turn