Come on Motion!
Manhattan cannot possibly be experienced in a single day (or in a lifetime for that matter).
You could easily kill 4-5 hours inside any one of the Guggenheim Museum, the Museum of Modern Art, The Metropolitan Museum of Art, the American Museum of Natural History, the New York Historical Society, The Frick Collection, The Whitney Museum, the Neue Galerie. Any one of those is worth the trip, and you can ride the subway up there from Penn Station. Take the E train to 53rd street to get to MoMa, for example. ($2.50 per person, you can buy a MetroCard at the station).
Man even with the cold weather anything beats sitting around at JFK in the low humidity.