My favorite is Calypso Cafe - 5211 S. Harper Ave. (in Harper Court - bring quarters for metered parking) 773-955-0229 - I recomend the plantain nachos (not 100% sure they are vegetarian though)
I've also had good experiences at:
Dixie Kitchen (right across from Calypso - owned by the same folks I think) 773-363-4943 (southern food)
Mellow Yellow 1508 E. 53rd St. 773-667-2000 (I always end up getting the crepes, even when I go there to get chili, I just can't resist)
Snail Thai - 1649 East 55th 773 667 5423 arguably the best Thai in Hyde Park. That's not saying a great deal, but I like it, so I thought I'd add it here.
Places other people like that I don't:
Medici (I mean, at some point if you live in Hyde Park I guess you have to eat here, but I'm not too sure why you'd have to go back - except for the strawberry lemonade - if you really want to contribute to this Hyde Park institution, go get a sandwich at the University Market next door, or pick up some baked goods at the Med Bakery - all owned by the same folk)
Cedars of Lebanon (I'm really frustrated that I haven't had a good experience here, everyone I know enjoys it)
I really want to go to La Petite Folie at 1504 E. 55th St. (in the courtyard adjacent to the Co-Op and Wallgreens at 55th and Lake Park - french cuisine) but when I lived in Hyde Park I couldn't afford it, and now that I'm out, I always have somewhere else in mind for a dinner like that (although rumors that one of my favorite professors occasionally cooks there might get me to come in) 773-493-1394