If you can take getting a little wet I still would recommend heading down to Beavertail or at least doing Ocean Drive in Newport and stop at Breton Point. It's still nice to be by the water even when it is cold and wet, at least for me.

The Audrain Auto Museum is pretty cool, and you could combine that with a mansion or two. Then you could head over to Broadway (as mentioned Fastnet or Pour Judgement or other places) and see what you like there, or head down to Thames. Go to the brick Alley and get some comfort food. Whatever.