Boston isn't an hour from Amesbury unless you drive very slowly.
Take the T in. It's easier. Just make sure you know what time the last trains are.
I'm from a few towns over (in NH) from Amesbury.
Last time I was there - Boylston Street stop (Green line) had a lot to do - the green line also runs past North Station and into the museums. I think the Orange line also runs by Northeastern Univ and a few museums.