Try booking Fishermen's Memorial State Park and Campground, down the road is the beaches in Narragansett. If you bring bikes, you can bike down the road to the ferry and take it over to scenic Block Island and bike the island, lots of touristy shops and restaurants to get a bite to eat. From the campground is easy Day trips to Newport Mansions and Mystic Seaport CT, about 40 minutes away. Check out USS NAUTILUS museum in New London, CT
You can also drive & park at the ferry and rent bikes or Scooters at Block Island.
Mike