Take Route 114S from East Providence from either Route 195 or Route 6. This takes you through the centers of both Barrington and Bristol which can be a little congested at times.
Once you get to the southern end of Bristol you will take the Mt Hope Bridge to the Aquidneck Island. Once on the island you can take either 114 or 138 towards Newport. Once in Newport make sure you take Bellevue Ave past the mansions to Ocean Ave.
Ocean Ave is a very curvy road that follows the coastline to Bretton Point State Park.