I'm not sure about Amtrak service, but I know Canadian Pacific, Norfolk Southern, and NYS&W run a lot of freight around there. Amtrak often uses trackage rights with the freight companies, so I would imagine there's passenger service in the vicinity.

No, none at all at the present time, unfortunately. Many residents would like a passenger train service to New York City but at the moment they have to use the bus. Nearest rail station is Syracuse, a long way away (70 or so miles).

You'd have to get NJTransit into NYC then Greyhound bus out from Port Authority Bus Terminal, over 4 hours journey.

If you can go by car it's much easier: From New Jersey

(New Jersey Turnpike North) to Route 280 WEST, then take I-80 WEST to Route 380 North. Proceed to I-81 NORTH to Route 17 WEST. Take Route 17 WEST to Exit 70 SOUTH. Follow Route 201 and the SUNY signs, crossing bridge to Route 434 EAST. The main entrance to campus is your first right.