Gudday and welcome, Nancyo
Futher to what's already been said, I reiterate Ron's suggestion of Healesville Sanctuary to the northeast of Melbourne if you get the time; a much better option than Melbourne Zoo, which is fairly generic. You'll probably need to hire a car to get to Healesville tho.
Other good Melbourne stuff would be Brunswick St in Fitzroy for good food and CD shops, ditto Carlton, St Kilda and Richmond (inner subs) for good food. Consider a ferry ride to Williamstown, a nice old part of Melb with great foreshore, pubs and restaurants. A tram to St Kilda beach from the centre of town gets you to a beach and the Esplanade pub, well worth it.
Only go the Melbourne Museum if you're really stuck for something to do, it's fairly dull - although I might have a slightly biased view on this having to work here every day
Good Ocean (ie. not bayside) beaches at Gunnamatta and Great Ocean Road, but once again, only practical if you have a car and a few days.
Melbourne public transport is being spruced up for the coming Commonwealth Games, but it still isn't too flash to be honest (trams, buses and trains). Go and see a game of real football at the MCG if there's one on (not sure when the season starts this year).
Hope you have fun, and don't forget the sunscreen!
Ron, Canberra for a first-time visitor to Aus? 
(joke)
CTB
