if you want funky and hip type suburb then St.Kilda is probably the one, its got all types of people and variety in housing for rent or purchase. its close to everything that you would like and very central for easy travel by car tram and rail. plenty of pubs clubs etc. grand prix time is near your arrival and right on your doorstep.
otherwise consider places like Richmond, Carlton, Collingwood,Fitzroy,Brunswick. each have that something different.
even try something as simple as looking in travel guides to get an idea about the type of place you want. then buy the trusty MELWAYS everyone in melbourne has one all ads and references give Mel.Ref numbers for easy finding. it will show you just how far/close places are apart.

last of all enjoy the place.
i love melbourne, miss it heaps since leaving for brisbane april 07. brisbane is so damn lame in comparison. i regret leaving, but i dont miss wall to wall AFL you'd think other sports never existed if not for 5 second score reports on the news.

sounds funny considering the suburbs i reccommended.
cheers mate enjoy.

Hi there, I've lived in Melbourne for 7 years and thought I could give you some advise.
"A young, hip, vibrant, culture..up beat.. lively suburb" sounds like Brunswick or North Fitzroy to me, there is fantastic nightlife and live music scene down Brunswick Street.

The rent will vary depending on the location and type of property from $125 - $300 a week unless you find a sharehouse with a bunch of students or something along those lines. Check out Domain or sharehouse accomodation sites to find a place to stay or even post an ad on cracker under the Realestate - Accomodation wanted section. I am currently looking for a place to stay and this is what I've done.

My email is ketiara@gmail.com if you want a melbourne insider before you make the move.

Good luck! =)