Lots of choices for ski/snowboard areas the farther north you get. Living in NJ the closest I can think of(not counting the ones in NJ, not worth going to) are...
PA: Jack Frost/Big Boulder, Camelback
http://www.skipa.com/
NY: Hunter, Windham
http://www.onthesnow.com/NY/skireport.html
Then the best areas are going to be up in the Vermont area, at least as far as the NE goes. Can't help you as far as train access goes, but if you check out indiviual sites I'm sure you can find the info you need.