Im not from Melbourne so Im sure there are lots more than the few below, these are our favourites, all scattered around strategically positioned near sisters/brothers/inlaws etc. and get visited every time we go.
Deadman Espresso -South Melb: awesome coffee and food (French toast was amazing, but $17), cool vibe in there too.
St Ali - South Melb: just round the corner from Deadman, everything is good.
Liar Liar - Hawthorn: had some very tasty breakfasts here a few times, not the biggest place so can be pretty full. Service was always good, had 6 of us order breakfast/drinks/coffee with very particularly picky dietary requirements/changes to 3 of the meals, the girl had no notepad and everything came out at the same time without 1 mistake, I was impressed.
Proud Mary - Collingwood: This place churns out great coffee and food, can get very busy and have been put on seating reserve lists a few times, but well worth the wait. you also get to dribble all over one of the only (I think) 6 group Synessos in the world.
Brother Baba Budan - CBD: Its tucked away and I dont think they really do breakfast, but an awesome place to stop. Theres seating right behind the barista so you can sit there and watch them work away, which is very cool.
Theres some to get you started anyway.