Lincoln Woods State Park is a nice little oasis not too far from Providence. A decent portion of the park is taken up by Olney Pond, the name of which is slightly deceptive since the body of water is large enough that the park does allow boats. Canoes and the like are probably your best option though, as only boat motors under 10 horsepower are allowed, and even those are not allowed on weekends during the summer season.
Swimming and tanning on the beach are an even better way to enjoy the water at the park. Lincoln Woods boasts a very nice, sandy beach, something hard to find on the rocky shores of New England. Lifeguards are on patrol in season and there are showers and a concession stand only feet away. Elsewhere in the park there are almost 100 picnic sites available and plenty of space for hiking and biking. You may have a problem if you want to play a game of soccer or softball though, as the fields often seem to be occupied by local leagues.