I second Rose Garden! My regular eatery when I''m lazy to cook!
But I'll NEVER ever step into Shanghai Dumpling again! It has been shut down several times due to hygiene problem (e.g. rats and roaches). And the last time I went there, service was DAMN BAD! Please do not ruin your Melbourne trip because of this...
Try Nasi Lemak House along Cardigan Street, adjacent to Grattan Street. Another of my favourite eatery!
Lanna Thai along Flemington Road adjacent Villiers Street is also good! But a bit on the expensive end...
Another must-try for me is the bratwurst at Queen Victoria Market! You can't miss it if you're there cos' it's always having a long queue!
For fast food, try Grill'D and Nandos! Once you tried the Nandos there, you wouldn't want to try the one in Singapore!
Have fun!