I have often been asked by friends where they should visit in Australia & I am afraid if I do recommend Melbourne it is someway down the list only to be visited if the trip's duration is likely to exceed 2 weeks. I would always put Sydney, Cairns & Ayers Rock above Melbourne as they offer sights and experiences which are unique to Australia.

I am great believer that cities are similar wherever you travel. Most have zoos, plenty have botanical gardens & all of them have shopping & clubs. Sydney is one city worth visiting as it has a unique harbour but I am afraid despite its agreeable ambience I would only recommend Melbourne when an important event is on such as the Australian Open or Melbourne Cup.
Obviously being a young country Australia can not offer many places of historical interest. I do think it could do with some better historical museums -The Immigration museum in Melbourne is a particularily insipid establishment. There is absolutely nothing wrong with highlighting the locations with interesting exhibits on Australia's convict heritage.