under $20 means probably a cafe, or a light dinner, unless you just get an entree, and maybe a soda or drink tap water. i would say just walk around, see what suits your fancy, check out the menu before going in, and take it from there. NYC has so many choices, and restaurants open and close all the time due to the high rents and other influences, so i would just see what you find, that’s convenient and meets your criteria. if you want to travel a bit, go down to Chinatown, Little Italy or Soho for more choices. These places are all accessible by a short subway ride. Subways are everywhere, stops about every 8 blocks.
if you meant the entree has to be under $20, you have more choices.
if you’re into ethnic food, you can always pick up a falafel or something like that off a stand.
during the holiday season, you are going to enjoy just window shopping and taking in the festivities and decorations. you are going to come away feeling like you were in a holiday wonderland.