There are plenty of choices in Chinatown if it's within your range: soup noodles, dumplings (decent 水餃 or maybe 湯包, although 鍋貼 are not good quality), steam buns (包), Southern (粵)-style breakfast items and lunch specials ($5.75 at Amazing 66), jook, 豆花, roast meats (well, 串燒 from a cart is a waste), etc. Just walk up Mott St or along Bayard and see what suits you. There are some Vietnamese and 潮州 eateries worth mentioning too (please search this forum). If you venture further east, there are a couple great 福州 places for pull noodles, soups, and caseroles (speaking some Chinese, either putonghua or the native dialect, is pretty much necessary there, and be warned: they allow smoking inside!)
All your heart desires for under $10, a $1 tip is considered good. Happy eating!
Also, there is an oriental fruit market along Canal and on to Mulberry: get some!
If you need a specific recommendation in any category, please search this forum or post your question here.
66 Mott St, New York, NY 10013