There are bathrooms with hot showers (25 cents for two minutes). There are pumps scattered around the campsites for water and a camp store at which you can buy supplies. There is a small lake (or is it a pond?), but the ocean is much nicer. The ocean is about a mile from the park, an easy walk or drive.
Driving directions: Take Interstate 95 North to exit 92 in Connecticut. At the bottom of the exit ramp, turn right onto Connecticut Route 2. After 2.5 miles, turn right onto Connecticut Route 78 East. Follow 78 East until it ends, and then turn left onto U.S. Route 1 North (also known as Post Road). After 6 miles look for the entrance to Burlingame State Park
Address: 1 Burlingame State Park, Charlestown RI, 02813
Phone: 401-322-7337 or 401-322-7994
More info:
http://www.riparks.com/burlingmcamp.htm