Montauk Bar (incongruously named after a small beach town at the tip of Long Island) is a pretty good bet for a decent cocktail in a very nice setting.
Atmosphere: After coming from a crappy dive bar, Montauk was an oasis of clean concrete and filament bulbs. There's a nice bar area with a bunch of table seating as well. It's not huge so I can imagine it fills up as the night goes on. We were there a bit on the early side of a Saturday night and the vibe was pretty laid back.
Drinks: Cheaper than the aforementioned crappy dive bar which was a definite plus. They were all kind of a little weird though... not bad per se... but just different. We ordered a couple of classic cocktails (a Sazerac and the Last Word) both of which we've had many many times before. The Last Word was relatively true to the original, but the Sazerac was... strange... again... not altogether bad... just not as expected.
In any case, we had a good experience here and would for sure come back if ever we're in the The Great White North.