Sounds as though the locale is more important than the food. The place that fits the bill perfectly, IMHO, is the Frying Pan, which is located on a barge along the Hudson River in Chelsea (adjacent to 26th St.). Believe it is Pier 62. Always a crowd, but it is definitely cheap and definitely funky.
The Frying Pan
12th Ave and W 26th St, New York, NY 10001