There are lots of apartments in Melbourne ranging in price from cheap - which tend to be in the eastern area of city, I think - and up to luxury. Our group has booked at a mid-range apt - quite snazzy - right near the centre as we have a couple of littlies with us. It's $300/night for a two bedroom apt. You can get 2 bedroom apts for under $150/night if you look around, however (if you've people to share with this could work out very cheap).
Just look on Wotif and check out the maps to see where they are relative to the centre. it's on a tram line, which makes it a bit easier, too.