Why not have drinks at Gotham? They have a very good bar.I've gone there for drinks before walking across the street to have dinner at Strip House.If you definitely want to go somewhere else before dinner( I like doing that also) then you can't go wrong with the already mentioned Flatiron Lounge and Gramercy Tavern.I also like Flute(right next to Gramercy) and haven't been to but have heard good things about Rye House and Raines Law Room. All within a short walk to Gotham.
37 W 19th St, New York, NY 10011
Raines Law Room
48 W 17th St, New York, NY 10011
11 W 17th St, New York, NY 10011