I've been to three relatively new tea joints in downtown New York recently. The bad news is that two of them were such that I didn't even bother to sit down and order some tea. One of them is a keeper, though.
Sanctuary T, at 337B West Broadway at Grand St., is basically a typical swanky SoHo bar/restaurant/café with a tea around the edges. They seem to use tea in some of the food recipes, if that appeals to you, but there are very few unflavored teas on the menu, and nobody was drinking tea when I happened by on a weekend afternoon.
Gramstand, at 214 Ave. A between 13th and 14th, is a hipsterish place that serves tea among other things, but not many varieties and, once again, most are flavored. What really discouraged me was that they store their teas in lucite containers.
Saving the best for last, there's Amai Tea and Bake House, at 171 3rd Ave. between 16th and 17th. It's a very peaceful, pleasant room to sit in. The tea selection isn't large, but the unflavored teas seem well-chosen and fresh. My wife and I had a lively Makaibari second flush that must have been this year's and a not-too-subtle but quite fresh maofeng from Lincang county, Yunnan. They serve the teas in Bee House pots so you can avoid oversteeping. What's really remarkable is their sweets: baked goods that tend toward dense textures and deep flavors, not oversweet. Even if I hated tea, I'd go there for dessert. Their prices are moderate.
/Lew