I'll second Possum's comments. There's no need to eat badly in Melbourne - even on a budget. The city and surrounding suburbs are overflowing with excellent, well-priced cafes etc. The food court at Southbank is a good cheap option as well.

Melbourne has some of the best cheapest restaurants in Australia. Give one of the Vietnamese Restaurants in Victoria Street, Richmond a try. The Vao Doi Restaurant is almost an institution, or try Quan 88. Richmond is only a short distance from the city and very easy to get to on a tram.