There is no direct train to Williamstown but there are a number of services that will get you close.
Amtrak Albany, NY (ALB) – A variety of Amtrak lines stop at the Albany-Rensselaer train station. From the station, it’s about a one hour drive east to Williamstown.
MetroNorth, out of Grand Central Stations, will get you as far as Wassaic, NY at a reasonable cost. From the station it’s about a 2 hour trip northeast to Williamstown.
Amtrak Pittsfield (PIT) – Limited service on the Lake Shore Limited line.