Which mountains (or hills) are visible from both Boston and Rhode Island?
As Boston and Rhode Island are whole areas more than points, the question is easier to answer the other way around: From which mountain you can see Boston and Rhode Island?

To answer the question I'll use the SRTM Digital Elevation Model at 30 meters resolution, and pick the following five mountains or hills that seem good candidates:



Shown elevations are the ones derived from STRM data. From each of these points I've made a view shed analysis. And for easier comparison I've put them together in the following animation:



In these view shed analysis, the areas in read represent the one that would be visible from the corresponding mountain or hill. As you can see, Blue Hill and Moose hill are visible from some parts of Boston and Rhode Island. So that chain of hills (including Tower Hill) is definitely visible from many parts of both areas.

For the mountains further inland as Wachusett Mt. and Monadnock Mt., they don't seem to be visible from the coastal areas of Rhode Island.