We just got a license from the Town of Narr, and that was pretty much good anywhere. The beaches in RI are public property up to the high tide line, so you can get married on them no problem--you just have to be OK with the random public in your ceremony pictures.
You have to get approval from the Park and Recreation board. They don't allow beach weddings from Memorial Day to Labor Day...but they have special permission forms they will mail or fax you if you call their office. Then they review it and give you their answer. I believe you have to specify which beach you want to have it on out of the 4-5 beaches they control.
I got married at Scarborough Beach this past Sept. I had to fill out a form through Fishermans State Park Office (they were in charge of Scarborough through the winters) and wait for their approval. We got married on the lawn at the southernmost end of the beach & it was absolutely beautiful (also free, which is a perk!) and it was late Sep so there were no onlookers or beachgoers. The only thing was that I asked the workers at Fishermans State to open the gate 2 hours before my ceremony started and they promised they would but never did (I called to remind them 2 days before the wedding and even the morning of - ugh!) so parking was tough for everyone - especially the limo driver since the gate wasn't open. Let me know if you have any questions..