Lodging: Best bet while in college is to shack up with friends. Short of that, you're talking about NYC hotels - take your pick.
To Financial District: The subway is safe (try the A/E blue-colored line), but for convenience you just might want to cab it.
To JFK: Take a cab and donate the $40 to charity. Or, plan for an hour and a half for the subway on $1.50. JFK/Aqueduct stop.
Christmas Spirit: The Rockefeller Center tree and rink are about as Christmas-y as you can get in the City. A good place to eat on the cheap-good-much triad (and pretty healthy) is Benny's Burritos. In fact, you as a college student would do well in that part of town (Greenwich Village). For a Chapter House-esque experience, try Chumley's at 86 Bedford Street (do look for the street number).
Also, while you're around Rockefeller Center, stop by the Cornell Club on 44th Street between Madison and Fifth.
Good luck on your prelims