I've been to Connecticut many times during my many summer vacations to Rhode Island. Connecticut is just a hop, skip, and a jump away from Rhode Island which makes it an easy place to visit. Although most places near Rhode Island are very easy to get to.
I've specifically been to Mystic and Foxwoods.Mystic is a cute little down, with a bunch of cute little shops. Last time I was there was July 2008. I went with my aunt Margaret, my cousin Charlene, and my God-daughter Katherine to the Mystic Aquarium. I have a thing for Aquarium's, and this one was really nice. It was outdoors, and had lots of interesting and fun sea life. Katherine was a year and a half and all over the place. She loved running to all the different "stations" pointing to the fishes and then running to the next display while laughing because us older folk couldn't keep up!
Foxwoods is this huge casino in Connecticut. The best way to describe it: It's the Las Vegas of the East. It's gorgeous. Although, what makes this place so amazing is the drive. It's about a 40 minute drive from W. Greenwich, RI. The drive is very remote, as if you are heading off to the middle of nowhere. And then, you see it! All the lights and glitz! It's stunning! Words just can't do it justice.