For a relaxing cup of tea, you might consider this attractive East Village tea house. It is owned by T.I.C. Group, which also owns an insane number of other Japanese restaurants in the immediate area.
For example: Sobaya (for soba, a type of noodle), Robataya NY (a grilling specialty), Otafuku (whose menu includes octopus balls and savory pancakes), Decibel (a sake bar), Hasaki (for sushi), Curry-Ya (for curry!), Rairai Ken (specialties of ramen and gyoza, a type of dumpling), and Shabu-Tatsu (for shabu shabu and Japanese barbeque). That’s a lot!
At Cha-An you can browse through an extensive tea menu, complete with pictures and explanations. I visited in early 2011, armed with Japanese books, and practiced converting transliterated sentences into kana while sipping my beverage and occasionally making out Japanese words spoken by employees behind the counter.
If you live in the East Village, this would probably be a great place to frequent for Japanese practice.
On an unrelated note, during the months I studied Japanese I noticed that the toilet technology of Japanese organizations and businesses far exceeds that of comparable American establishments. When you enter the bathroom at Cha-An, the toilet rises to greet you. I was impressed.
Cha-An Tea House
230 East 9th Street, 2nd Floor
(between 2nd and 3rd avenues)
New York, NY 10003