Karia, if you're in NJ there's an excellent tea place in Montclair- I assume if you're close enough to NY you're in North Jersey:http://www.southsilkroad.com/
This is a link to their retail site, but they have a store on Church Street that you can buy tea, as well as have a cup. They also have small sweets to snack on and a huge variety of tea. It's right across the street from the fabulous Montclair Bookstore, if you're so inclined.
I was about to post about my favorite place in the city, and really the only place I know since I don't make it into the city very often anymore- Amai Tea House. Looking at the website, they actually just annouced their closing. Very sad! I did a review of this place a couple of years ago. You can still purchase their cookies though it looks like from their website.