You can dive at the Waterford boat launch although I would avoid it when there is alot of boat traffic. We typically do it at night when most of the boaters are gone. You aren't technically supposed to dive there but it's regularly patrolled and nobody has given us a hard time about it. It's about 10-12 feet deep.
Eastern Point is another place you can dive, but in the summer season they charge $20/car to get in. We dive there before and after the beach season when there is free parking. It's on the eastern side of the Thames river at the mouth of the river. As you go out into the river I think the max depth we hit was about 20 feet. There is a rock line that runs south that is easy to follow.
Then there is Stonington Point. From what I understand there is some town ordinance that prohibits diving in the daytime. I don't know this for sure though, we always go at night here.