Have you checked out wotif and the like?

I've stayed at lots of places but I can't quite remember the names apart from the popular ones like sofitel, park hyatt, grand hyatt, crown... but I've also stayed at other little ones that were just as good.

I would say try and get a serviced apartment if you can with 2 rooms. Or somewhere with a big room that has a sofa in the lounge that is seperate? You can also get two rooms that connect and have a door between that can stay open at all times.

I've yet to find a bad stay in Melbourne, even for a budget price.