Blackstone River Bikeway.

Any Rhode Islander would laugh at the notion of "the Narragansett/Newport area." Those are on opposite sides of the bay, and take two bridges and at least 25 minutes driving. That's a long day trip to RI sensibilities.

I'm not current on the current bars and museums in the area. I like much of the coastal attractions in the rain, just as well as in the sun, so can't really help on that end, other than to suggest you not discount outdoor things just because it's raining.