There's plenty of fun things to do in Newport, Rhode Island, which is only about a thirty minute drive from Bristol. A few suggestions: Cliff Walk: You can walk along the ocean, where there are really pretty views of the water, and of many of the Newport mansions. Breakers: The Breakers was the summer house of the Vanderbilts, and is a fascinating look at the peak of early 20th century luxury. International Tennis Hall of Fame: (Bradley's suggestion, Maayan says this is a waste of time). If you're a real tennis nut, this is a really interesting spot. Touro Synagogue: This is the oldest synagogue in the United States, and it is still operating today! It's an Orthodox congregation these days, so they won't give tours on Saturdays.
Providence is a fun little city to spend an afternoon in. Here are a few of our favorite spots: Roger Williams Park/Zoo: It's the best zoo in New England (Maayan went to camp here for many years and loves the Moon Bears) Rhode Island School of Design Museum: This is a cute art museum in downtown Providence Brown University: Enjoy the ivy-filled environs of this university (and maybe get some early college searching in for your high school student.
Colt State: A beautiful park along Narragansett Bay, a beautiful place for a picnic or walk. Blithewold: The Blithewold mansion and gardens are gorgeous to walk through. Herreshoff Marine Museum: For the naval nerds among you can learn about the marine history of the area, and especially about the America Cup yacht race.