How long do you have? That kind of frames the geography you can reasonably see in New England.
I’d, of course, spend time in Boston. What you do there depends on what you like to see. The museums are great, so if you like that, The Boston Museum of Fine Arts and the Isabella Gardner Museum are definitely high on the list.
I never leave Boston without a meal or two in the North End. The Italian restaurants there are still good.
Boston is a walkable city. You can walk from Fenway Park, through the Pubic Gardens and the Commons and into the North End if you are in any reasonable shape.The Gardens and the Commons are always nice to see. I am still partial to the corny Swan Boats
The Cape is always a great place to see, BUT even in September you can get a lot of crowded traffic. (Especially on weekends) I would take the Ferry (90 minutes) out from Boston to Provincetown, which is the artistic fringe capital of the Cape.
Speaking of ships, go see the USS Constitution (also walkable), the oldest commissioned ship in the world.
Newport Rhode Island is a great place for the mansions (Vanderbilt, et al) and a harbor that cannot be beat. Beautiful place for just hanging around.
I’m less familiar with New Hampshire and Vermont, so I’ll leave that to others. I’ll think a bit about Maine, as the coast is always nice and the seafood is also great, but a specific spot does not come to mind right away.