Tarralucci e Vino on 19th between Broadway & 5th. They serve food also but don't generally have issues with people sitting for just drinks. This would be a great low-key place for wine and appetizers.
Barna on Park and 26th in the Giraffe Hotel basement.
Japonais on 17th (or maybe it's 18th?) between Park and Irving. They have a lounge area upstairs.
Sugarcane next to Shushisamba on Park, but they tend to get very crowded.
My top pick would be Flatiron Lounge, though
Went to the The House. Beautiful place, great wine (we each did a half bottle of a white and got a bottle of champagne) and they do a super cheese plate paired with different honey and fruit paste for each one. excellent bread basket. Went to Flatiron after. Thanks for the advice!
A new wine bar called Wined Up is on 20th street and broadway above the restaurant Punch. Supposed to be pretty good.
I would say drinks at the Gramercy Tavern bar but that will probably be packed.
Metrocafe and Wine Bar has a really nice log wooden bar where you can get flights of wine.
There's also always Olives Bar in the W Hotel in Union Square.....Or I think I may have it--a new place called The House opened on Irving place and 15th street. While I didn't enjoy the food there, the bar is beautiful and thay have some nice glasses of wine. Here's the link: