There are two (2) casinos in the area. Mohegan Sun and Foxwoods. It's to early to see what their entertainment schedule is.
The Mystic Seaport is a historic place. Mystic Pizza has good, and unusual pizza.
The Coast Guard academy is across from the Navy base.
There are many sailing ships, tall ships, that people can spend time on.
It may be possible to get a dinner cruise on one of them.
http://www.mysticwhalercruises.com/
http://www.privateerlynx.com/