If you're looking to be west of the Providence metro (more towards CT) look at Chepachet, Coventry, or Hope, RI (the "town center" of Scituate). Coventry and Hope are close together, connected by Route 116. West Warwick is right there too but that's more east and more urban. The old factory towns have some nice old houses with large rooms, and they go for cheap money since its not exactly prime location now that most of the mills are closed now. Its sorta like being in town but also being out there a bit since you have the rivers flowing through town (where the factory is) and just beyond the village, its the woods.
If you can find an apartment on the first floor, you may get the basement area with it. There are also mill cottages which are pretty convenient, usually 3 bedrooms on each side of the duplex. If you want to be way way out in the sticks, it will be more expensive and fewer rentals to be found. Hope that helps!