It is probably easiest to join a club. Springfield Sportsmans has a caretaker that lives on site and does the memberships so you might be able to join on the spot with cash. I know I did a few years ago. A few other in the area are Fairview in Chicopee, Chicopee Sportsmans in Granby and Westfield Sportsmans in Westfield.
I would not go to just any place right now with a shotgun to shoot as it is currently deer season and if you are near the woods with a shotgun and no license or orange on you will be cited for hunting violations if checked.