The areas with the most Republican support tend to be the very rural (by RI standards) towns of the RI/CT border. Whenever a town votes Republican in presidential elections it is always a town from this region. Almost all of the Republican representation in our legislature comes from this area as well.
This area is inhabited by "swamp yankees" which is a phrase used to describe WASPs along the RI/CT border. This area tends to have less Roman Catholics and "ethnic" whites which makes it different from the rest of RI which is inhabited by Roman Catholic Italians, Irish, Portuguese and French-Canadians.
Isn't East Greenwick very Republican too?
They tend to be very upper-middle-class.
Same with the Portsmouth/Bristol/Barrington region.
Somewhat with Smithfield/Lincoln too, and Warwick.
Along with the western region, as you mentioned.
Not sure how that happened, though.
Yet like I said, the Republicans only have 6 seats in the 38-member Senate and 6 seats in the 75-member House.
So I really wouldn't say the Republicans in RI have a base region at all.
Here's a map to see: