Cause I'm a gypsy, are you coming with me?
Yes, I'm sorry, I just quoted Shakira... Judge me!
After living in Madrid for 10 years, its inevitable to get used to certain things such as lunch at 3 pm and dinner at 10-11 pm, going out at 3 am and getting home at 8 am, something you won't be able to do in the US.
In NYC for example, I can brag about restaurants, shopping, locations, vibes, ambience, and a large list of positive things, but when it comes to night life, I love you NYC but Madrid is way ahead of your game.
Nonetheless, I have a few favorite spots which include Le Bain & Boom Boom room, Soho House, Milk & Honey, Raines Law Room, Cafe Select, Gold Bar, La Esquina, Paul's Baby Grand, almost all of their rooftops (what can I say, the views!) specially The Nomad (naturally :P), Upstairs at The Kimberly Hotel, PHD, 230 Fifth, Empire Hotel, among a few others.