If you plan to hit Mystic, CN and Newport, RI, then my suggestion would be to use Hartford, CT or Providence, RI, as the starting airport. Cape Cod can become a traffic jam in the summer so you might want to wave that one off. Albany, NY and Manchester, NH are two additional airports to consider (all of these mentioned thus far are serviced by SWA, as are a few others mentioned). I agree with avoiding Boston-Logan airport.

P.S. You might be able to purchase an EZ-Pass device to make traveling on toll roads easier. Sometimes they are hard to avoid. Oh, and have fun in Cooperstown!