outdoors cheap and funky
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