There is a cool cocktail lounge/library called Brandy Library or Distilled both a few blocks away.
There is a bar area but it is a bit loud and crowded. It's more for those waiting for a table.
They do have a bar area. There's also Smith and Mills across the street on North moore
The Hideaway Rebecca is close by on Duane, but if in the summer, the Loopy Doopy rooftop in the Conrad is a better choice, though it's small and seats are limited and sometimes it's windy. Not exactly fun for ladies with skirts and big hats.
Smith & Mills is cozy.. there's also a bar at Tribeca grill. There is a bar at Locanda Verde.
Thanks! Your answer is awaiting moderation.