Try Cozy Soup N. Burger on Broadway and Astor Place in the Village. Its been featured in a few movies and has always been a place to go late at night. As a vegetarian I'm not sure what they might have for you (I'm a carnivore myself) but they do have salads, appetizers and stuff, plus a nice selection of soup, try the split pea or lentil! Its a greasy spoon, but its comfort food is tasty and filling.
FIrst, the Korean restaurants in "Little Korea", 32nd Street between Broadway and Fifth, are virtually all open 24 hours a day. There are dozens of options, and while the Korean BBQ is the hightlight, there are nurmeous vegetarian options including the famed scallion pancakes, veggie Bi Bim Bap (a rice dish), tofu dishes and the like. New Wonjo Restaurant is my favorite on that street but there are literally dozens of options.
If you eat fish, there are a number of late night sushi places, the best being Sushi Seki, on First Avenue between 61-62, which is open until 3 A.M. on some nights.
Great NY Noodletown, 28 Bowery in Chinatown, is open until 4 a.m., famous for its noodles and BBQ meats, but there is great Congee (a stick to your ribs rice porridge) which can be plain served with fried dough, or with meat or fish and is great after a night of drinking.
Cafeteria, 119 7th Avenue at 18th Street, very hip and ecletic food (24 hours)
Veselka, 144 Second Avenue in the Village for Ukranian food including Borsht (Beet soup), potato Piroggi (dumpilings) and lots of breakfast options for late night dining (24 hours)
Mamoun's Falafel, 2 locations in the Village, one on St. Marks, is opened until 5am, been eating their sandwiches since high school (a long long time ago)
Hope this helps, Enjoy
