Hammonasset Beach State Park
Hammonasset Beach State Park, near Madison, lies adjacent to the Hammonasset Natural Area Preserve and offers over two miles of shoreline, a boardwalk, picnic tables and shelters, showers, a nature center, surf chairs, and a campground. Here is their website. Phone 203-245-2785 Map
? There are a number of trails including a paved one from the Meigs Point Nature Center. I think these may be accessible, but it would be wise to call the Park or the Nature Center (phone number 203-245-8743) before going.