When you're in NYC, don't bother with agencies. It doesn't work the same way as in Toronto.
That being said, 'Korea Town' is located on 32nd street between 5th Avenue and Greeley Square. There are tons, and I mean tons, of Korean students who are very open minded to spending a couple of nights with you in exchange for your assistance with their living expenses. Being Korean born, they are of a very 'male dominated society' mindset and so long as you're respectful and a bit romantic the odds are greatly in your favor. Pop into any of the Ramen or Kimchi places and invite any girl sitting alone to eat with you. This has worked for me more times than I can even count. Make sure you know something about Korean culture to begin a conversation and make them feel comfortable with you.
Maybe you'll keep in touch and maybe you won't but the very temporary arrangement is mutually beneficial since it's very discreet.
The process is interminably more fun and satisfying than calling an agency would be.