Sharon F&G has public trap and skeet every Sunday from 10AM onward. It's laid back there so you can learn . . . at least it used to be when I was a member some years ago.
Massapoag Sportsmen's Club in Sharon has matches frequently. The trap & skeet is open to the public, but it's fast paced and they will give you grief if you can't keep up the pace. It's a place for the really good shooters, not a place to learn or relax.
Braintree R&P has public trap on Sunday afternoons (after 12Noon).
No idea on prices at any place as it's been >15 years since I shot skeet or trap.