Fairway is an excellent mega-grocery store located in Manhattanville (neighborhood)Manhattanville at 12th Avenue and 132nd Street. The chain has several other locations, including one on Broadway between 75th and 74th street. True to its motto, Fairway is "like no other".
The store is huge and stocks almost everything, including an extensive cheese selection. The piece de resistance, however, is the 10,000 square foot 'cold room' for meat, fish, and dairy products. This alone is the size of one of the Morningside Heights' grocery stores. They provide jackets for you to put on when entering the room.
The only downside about Fairway is that it's a bit of a walk from campus. If you really don't want to walk on the way back, several van shuttles will take you. The Studebaker Shuttle has emerged as a particuarly attractive option, and may even stop directly at Fairway some day. Barnard also offers its students a weekly shuttle.