I live in Manhattan. Grand Central is closed from 2 a.m. to 5:30 a.m. and it is enforced. Bars in Manhattan close at 4 a.m. It is cold and dark this time of year. I would go with the airport hotel option suggested by a previous poster. Also, LGA airside is closed after the last flight of the night leaves. You can stay before security but be prepared to join multiple homeless people.