Similar to the whiteplanes suggestion, Signature at Morristown, KMMU, will shuttle
bus you to the local trainstation to NYC.  Its about a 30-40 minute trip into the city.
Trains leave hourly from 5am to 1am, more during rush hour.  Closest train stop would
be either Madison, NJ or Convent Station, NJ; either within 5 minutes shuttle bus ride.
Trains from there could take you to Penn Station.