Cycling Newark isn't my idea of a good time. Not only is it congested/city/industrial but the road conditions are really horrendous in the area. Manhattan is a world better by comparison.

http://www.njtransit.com/pdf/rail/Rail_System_Map.pdf

The Morristown or Gladstone lines look to be in the right direction, the end of those lines is pretty nice countryside too. You'll want to catch those lines out of Penn Station New York.