You can take Amtrak to Trenton or NJ Transit to Princeton, Princeton Junction or Trenton from Penn Station. To get there take Airtrain from terminal to Jamaica Station and LIRR or E subway to Penn Station. Amtrak to Trenton is 1 hour but costs about $35, NJ Transit is about 1.5 hours but half the cost. See www.njtransit.com for schedules and fares.
You can take Amtrak to