OP could fly to BDL (Hartford, CT). There are two newish Sheratons there, one at the airport, that aren't expensive. From there, get a cheap rental car (rates aren't bad at BDL IME) and drive north toward historic college towns like Amherst and Southhampton. The drive toward the southwest (for example, to New Haven, but there are pretty villages on the secondary roads) is also nice. You could even take the ferry to the tip of Long Island (Montauk Point) or the Bridgehamption to Port Jefferson ferry. Another alternative would be to head toward the mansions along the sea at Newport.

If Providence now has a Starwood (The Westin has been reflagged and is gone but IIRC a hotel is coming), fly/stay there and drive out to Cape Cod. It's easier than from BOS.