Within 20 minutes of your rental you'll find the historic seaport town of Newport and Cliff Walk, a 3-5 mile path between the famous Newport Mansions (must see's in themselves) and the Atlantic Ocean with spectacular views. Newport has great restaurants and bars, museums shopping and night life.
In Middletown, visit Sachuest Point National Wildlife Refuge, walk their trails along the Ocean. Adjacent to the Refuge are 2nd and 3rd beaches if you like a more secluded beach experience.
A10 minute drive across the Mt. Hope Bridge (which commands every view from all the south and west facing windows of your rental) is Bristol, RI another quaint seaport town, also featuring sensational restaurants and bars but in addition, you can take a ferry to Prudence Island and find endless miles of walking and bike trails.
Travel across the Sakonnet River Bridge (which you will see from every window facing south and east from your rental) and drive down the beautiful coast of the Sakonnet Passage (more fabulous vistas) for 15 miles through bucolic Tiverton, RI to the secluded hamlet of Little Compton. Tiverton has great walking/hiking trails at Fort Barton Woods, Weetamoo Woods and Audubon Emille Ruecker Wildlife Refuge. More sand beaches great for exploring can be had at Fogland Conservation Area and Fogland Beach.
Little Compton, another small RI seaport village boasts the finest winery in RI. Sakonnet Vineyards hosts tastings and concerts on weekend afternoons. Multiple ocean beaches are found on the southern end and some historic places to learn about the history of the area are available.
If you like golf there are three great courses nearby. Montaup CC, is private w/views of Narragansett Bay but allows public play. Green Valley, is more economical yet a top shelf track. For the ultimate golfing experience, play Newport National, ranked in Golf Digest as "The best course you can play in New England" which confirms it's public access.