I'd say, La Panella (for vegan donuts), Trippy Taco (for deliciious mexican) and Plush Pizza (for well uh.. pizza), would be my pick of vegan food in Melbourne that's pretty different to what you find interstate.
If you're into coffee, maybe go to Seven Seeds or BBB's. Ummm. If you're into records go to Missing Link or Round and Round. Minotaur in the city (among other places) for comics. Royal botanic gardens is great for walks/picnics.
That's stuff I like in Melbourne.. and would recommend to visitors.
Places like Smith St in Collingwood have heaps of restaurants that serve good vegan food. I would try Lentils as Anything in Abbotsford too, it's in a really nice setting and you can pay as much or as little as you like.