Cha An Japanese Tea House is my favorite NYC teahouse.
100% authentic, cozy, all the details perfect in that wabi sabi way. Not too pricey. Lots of matcha desserts and the 'set menu's' are delicious.http://www.yelp.com/biz/cha-an-new-yorkhttp://www.chaanteahouse.com
230 e 9th St, NY NY
It's cash only and no reservations, I usu try to go early ~5 or 6pm on a weekday.
(Edit: I had no idea Ippodo opened a store in New York! Can't wait to check it out. Thanks Pooblah.)