I began riding with the Wheelmen this spring and agree with all of the above. The club has been around for a long time and has the state well mapped out with all the suitable cycling roads indicated on a map produced, jointly by the club and the Rhode Island DOT, and available for free at any bike shop.
There seems to be a pocket of rural and lightly traveled roads in the Tiverton - Dartmouth area. I live in Bristol and ride there frequently. It is easy to put together a ride of 30 to 100 miles on pleasant country roads and the natives are friendly. PM if you would like to meet up for a ride there.