I don't know what schools are in NYC, but I am sure there are tons of them. If you are interested in full-contact, try to find a school or a gym that uses grappling techniques, like wrestling, BJJ, Judo, etc. But also incorportats striking. Many FC fighters study western boxing, kick-boxing, and many focus on Mauy Thai boxing. They also focus very heavily on BJJ, due to it's effectiveness on the ground, and wrestling for it's superior take-downs. I hope this helps in finding your school.
PS I think Renzo Gracie has an academy in NYC, that school would be an excelent place to learn and train, but might be a little costly