If you are staying in the CBD in Melbourne you could head down to the Yarra River (just cross it at St. Kilda Road) and they hire bikes there to ride along the Yarra Trail. It's pretty busy, especially weekends, but would give you a good gander at the city and surrounds. Bit hard if your other companions dont cycle though! You could always send them off to the art gallery or the museum! Not sure where you'd hire bikes out of the city though, except some bike shops, but if you only have 4 days you won't have much time for riding.
Maybe some of the hotels you stay in have gyms and you do a session on an exercise bike. I'm sure you will be doing lots of walking anyway, so that should keep you fit.
Hope you enjoy Australia.