Start near the Mass state line near Woonsocket, RI at the junction of Rt 146 and Rt 102. Take 102 South for around 35 miles, cross I-95, continue another 17 miles into Wickford, RI where you turn South on Rt 1A for about 4 miles, when you take a left, and get onto RT 138, in Plum Point, RI. You cross the bridge, cross Conanicut Island, and then go over a HUGE suspension toll bridge. Honestly: if heights, or bridges flip you out - DON'T take this route. Rt 138 brings you right into Downtown Newport. Voila!
The main goal of this route is to skip traffic, and the terror of trying to ride through Providence on RT 95. The bonus is that you really go through some lovely rural areas, and from Wickford on, you go through some gorgeous coastal towns. Newport is the destination, but there's tons of fun rides you can take from there, as well. You could have quite a happy weekend, riding around the shore areas, and visiting swanky mansions. You'll also pass over a HUGE suspension bridge - The Claiborne Pell/Newport Bridge.
Nice empty roads, until you get to the coast. Note the massive bridge for the fear-of-height-stricken phobics. Pretty flat and straight riding over-all but not conjested.
Newport is a major tourism draw, so expect tons of shops, eateries, mansions to tour. Beaches, lighthouses, and other attractions lie right outside of town. To mention a few: Green Animals is a topiary park to the north of town, right off of Rt 114. If you continue north on 114 you can visit the Haffenreffer Museum of Anthropology in Bristol. There's the International Tennis Hall of Fame museum in Newport itself.