Does anyone know some cozy and interesting places in New York City?

I'm going to New York in mid December for over ten days. I'm looking for some great places like bookstores, places to have brunch and other places which are worth to see but not necessairly mainstream. I don't mind outdoor places even in the winter up to 0 °F. :D Where would you go if you wanna relax, be inspired, have great conversations, or take a photo of awesome atmosphere? Please state address of the place and reasons why one should go there.

Public Comments

1. Check out Yaffa Cafe in the Lower East Side at St. Marks between First Ave and Ave A. Open 24/7, they serve beer and wine, a dark, relaxing place to grab a meal. http://nymag.com/listings/restaurant/yaffa-cafe/
2. the metropolitan museum, but if you want bookstores, barnes and nobles is your best bet where you can sit and read, while drinking coffee and even go on-line, though not all barnes and nobles are like that, try looking for the ones with the cyber cafes and sofas and stuff.
3. The Grey Dog's Coffee is a cozy, inspiring place. It is a little bit out of the way but can be quite a scene sometimes. You won't find many tourists there though and they have a good brunch. The original location is 33 Carmine Street between Avenue Of The Americas & Bedford St. They just opened up a second place at 90 University Place at 12th Street. Check out: http://www.yelp.com/biz/UDQNs4EOghsOoPuGsUoEzg