Hi...just up the street from Barnard on the same side of Broadway, near TiemannPl/124thSt, is a Middle Eastern deli that sells delicious tabouli, grilled chicken breast, hummos, etc -- only takeout i think, but wonderful stuff...
Generally however, i think Morningside Heights is a culinary wasteland...pizza?...i used to like those huge slices at Koronet (east side of Broadway, south of Columbia), and i have nice memories of the pizza at V&T on Amsterdam (but it's been severely criticized here and i haven't been there in ages so i can't give a solid rec)...
Sadly, i think you'll have to leave the neighborhood to get truly great chow...
Morningside Heights is by no means a culinary destination, but as a former Columbia grad student I managed to eat rather well while in school there. Here's a list of places worth checking out:
-- The Mill. Surprisingly decent Korean food. At Broadway and 113th.
-- Kitchenette. Good for home-cooking style lunch and brunch. 1272 Amsterdam.
-- Taqueria y Fonda. Outstanding Mexican food in a tiny hole-in-the wall. I still make the trip up there just for the rice and beans. 968 Amsterdam.
-- Max cafe. Great coffee drinks and light fare in a laid-back coffeehouse atmosphere. They make a good fritatta. Next to Kitchenette on Amsterdam.
-- Koronet Pizza. Definitely not the best quality, but their gigantic slice is just the thing to soak up the oceans of beer most undergrads suck down at nearby bars like the West End. A Columbia legend. 2848 Broadway.
gosh, i haven't really eaten anywhere in that hood since i graduated, but i second the fact that koronet, altho cheap, is one of the worst slices i have ever tasted. ollie's is sort of a staple, but if you go over to amsterdam, hamilton deli has great sandwiches and burgers. get the uncle sam. yum.
Agree with the previous posters. Max is particularly worth a try. Their lasagna is one of my citywide favorites.
Milano Market sandwiches ain't bad. East side of Broadway between 112-113th Streets. Nothing like the old Mama Joy's that used to occupy the spot. They had the best olive oil-soaked marinated sun dried tomatoes that I used to buy with mozzarella and fresh rolls to make my own sandwiches for lunch outside of Butler. Good times.
There is a little Japanese noodle shop called Saji's on 109th, just East of Broadway. An ex-girlfriend who grew up in Tokyo was addicted to their curry rice. (Then again, the alternative was the dining hall, so take that with a grain of fleur de sel.)
The new fried chicken and BBQ place on the corner of 109th (I think) and Broadway is promising. Only been there once, but I liked the mixed plate of chicken and baby back ribs quite a bit. The side dishes left something to be desired. The prices were a shade high for the student demographic, but managable (around $25 per person) for an occasional basis. If you're eating this sort of food more than once in a while, it's probably too much anyway.