There are a lot of chess programs for kids in New York City, in and out of schools. You might want to look at nychesskids.com.
I'm not sure how current this info is on P.S. 116, but if Bonnie Waitzkin is still reachable at the phone/email listed, she is a wonderful teacher, and incredibly sweet. She's great with kids of all ages, but I can't think of anybody better with really little kids, and I think it'd be a huge plus for a little girl to be taught by a woman.
(I'll PM you if I get a definitive contact for her.)
Edit for a P.S.: Bonnie was played by Joan Allen in the movie "Searching for Bobby Fischer" -- about having a chess-prodigy child (her son Josh), and how to nurture that kind of gift but still have a normal well-adjusted kid -- she has been a devoted chess teacher and coach in public schools for about 25 years, very generous, sweet and level-headed.