This is a very pleasant route from South Attleboro MBTA station to the beginning of the
Blackstone River Bikeway, entirely on quiet back roads and side streets:
http://goo.gl/maps/9RvKw Once you get on the Bikeway, you can ride 10 miles to Woonsocket. Some day, when Massachusetts gets its act together, it will go all the way to Worcester.
(Unfortunately, Woonsocket is a pretty depressing destination. I don't recommend spending much time there, unless you're going to the Museum of Work and Culture.)