Well congrats on being smart enough to not rent a car. December is going to be a bad time at any of the airports, but if you plan on staying in Manhattan, Newark is your best bet. However if you are staying in Queens or Brooklyn, you may want to consider JFK or Laguardia. If you go to JFK you have the option of taking the airtrain ($5 per person that you pay when you exit the train) and then hopping on the Long Island Railroad or the MTA (Regular Subway/Bus System). Warning-if your getting on the LIRR, make sure you purchase your tickets BEFORE you get on the train. Else, you will be subject to big fines.
Are you going to be traveling throughout NYC and it boroughs (Brooklyn, Queens, The Bronx, Staten Island)? If so, consider purchasing an unlimited metrocard. They come in daily, weekly and monthly flavors.