probably wouldn't want to stay around southern cross as there's not much around there.. go around brunswick st, smith st in the brunswick/collingwood area. heaps of vintage stores around that area which have a heap of random shit.
metropolis, readers and avenue are gr8 book stores. there's a heap of record stores around too.
use the train/tram to get around. really easy and cheap.
eating; coffee is pretty much good every where (my favourite is patricia's) and you'll be fine with zomato for cheaper places. try cumulus inc, tipo 00, cutler & co. those are mid tier joints. attica and brae but they're real $$$.
ngv is a must go