New York now has so many nice cafes and espresso bars serving high-end artisinal coffee locally roasted by Stumptown or Brooklyn Roasters etc, I'd think all these cafe's could source some quality tea but it's still hard to find.
I'm going to post a list of tea offerings I approve of from NYC/Bkln Coffee Shops, Cafe's, & Teahouses. Work in progress, I'm just posting the tea's I've tried so far which I find drinkable, so feel free to add!
Cha An: Everything
Grounded: Dragonwell, China Five Peaks (recommend this one)
(served in Mug with filter bag, or Teapot; free water refills for the pots)
Sweetleaf: Golden Yunnan
(Served in filter bags, you may ask for a mug)
Kinfolk: Oolong (unspecified, from In Pursuit of Tea)