Having lived in New England my whole life and also having stayed at all of the hotels mentioned many times, I'd personally stay away from the Providence and Hartford Sheratons as the "natural beauty" aspect is just not there unless you drive a while. Both are "side of the highway" Sheratons that cater mostly to business travelers. Side note is that I am actually very fond of the Hartford Sheraton as it has a very good club lounge and great staff. However, it's in the suburbs of Hartford.

If you're stuck on SPG and want a destination property, the Equinox has it hands down. It's in a mountain location in a cool, old New England town. You can hike, fish, shop, eat, or just relax by the fire pit. If the $$ or points are too rich for your blood, you could look at the others mentions plus the 4P on the cape.

It really depends if the OP wants mountain natural beauty or ocean natural beauty. If it's mountain, Equinox and So. Burlington (side of highway but short trip to mountains and Burlington is a cool little city) are good bets. If it's ocean, Portsmouth NH and Portland ME are good bets, both are awesome small cities with great food, drink, and shopping out the door and short excursions up the rocky coast lines.

If you don't want to play the SPG card, North Conway, NH is another good spot for natural beauty. Check out the Mt Washington hotel or North Conway hotels I miss having a SPG option there.

Ps.. Strictly opinion.