I'm North of Melbourne and it's very nice where we are. Freeway very handy and about 25 minutes to the city. Shopping centres within 15 minutes of me, north, south, east and west.
Lots of suburbs to choose from. The good thing is, public transport can take you pretty much anywhere.
If you want something close to the city, then you'd be looking at areas like, Carlton, Brunswick, Collingwood, Fitzroy, Richmond, Clifton Hill etc.
If you want something a bit further out, but still handy to the city via public transport. Then look at areas like, Moonee Ponds, Essendon and Strathmore in the north. In the east you've got areas like, Hawthorn, Fairfield and Kew. In the west you've got, Altona, Footscray and Flemington. In the south, St Kilda, Prahran and Toorak. All those areas are expensive as is the south-east corridor in general.
Other places you might like to look at are,
Doncaster, Coburg, Northcote, Preston, Heidelberg, Ascot Vale. All close to the city by train.
Failing that, try https://www.domain.com.au/Public/ChooseRegions.aspx?mode=rent&state=VIC