KO2,
I live in NYC and if you refer to the Shaolin temple on downtown on broadway I did go there to check it out. Not bad but the the Shaolin Temple in queens is more respected. The Venerable Goulin was Jet Li's teacher from what I am told.
But I think you should follow everyone's advice. From china town to midtown is martial art paradise in NYC Go to some schools and speak with the instructor to see if they are helpful with your questions. Remember teh type of instructor is important or more importatnt than the art becuase you are just starting.
I would strongly recommend Hapkido here is one link. A lot of the hapkido is taught with TKD. Wushu may be another good option it is very athletic. Also reaserch online what styles you are intersted. A boxing gym might also be a good start ( a real gym not "aerobic boxing or something), some of them will have Muay Thai classes also. I personally like Kingsway adn then Church street Boxing. Church street boxing is also in the same building as Vee Arnis Jujitsu and Machado Brazilian Jujitsu so look at them as well. There is a good Muay tai school at the Worlds gym on mercer street and 3rd street
http://www.worldmartial.com/
http://www.shaolin-overseas.org/
http://www.boxinghelp.com/new_york.html