I'd like to suggest that you get a travel guide to CT, select the items you have an interest in and then
inquire about those items. Any other method is depentdent on individuals knowing everything about the state.
There is a huge amount of things to do here for such a small state. We have all the colonial history, a seafaring history, there's a carosel horse museum, a submarine museum and every kind of museum in between, there's hunting, fishing, state parks, swimming, hiking, biking, sailing, clubbing, B&B's abounding.
Go to the state's tourism boards and have a look-
Visit Connecticut! The Official Connecticut State Vacation Guide
Connecticut River Valley Tourism - CT River Valley & Connecticut Shoreline Region Travel Tourism Visitor Information Guide
Mystic Country, Connecticut
There's at least 3 auto race tracks as well. Spend some time online looking.
Don't forget that we are equidistant between Boston and New York about 2 hours to either (+,-) Newport RI is just up the road and the mansions are a wonder to see.
I'd re-think visiting CT and think more about visiting New England as a whole. The states are small and have very reasonable highways (though there is congestion when and where you could expect it) so they are easy to travel through in no time. This isn't like the western states in size so travel time is nil compared to say; New Mexico or Utah. I can have breakfast in the Berkshire Mountains and be swimmning in the ocean that afternoon after driving at a reasonable rate and perhaps taking a side trip to Sturbridge Village or Mystic Village.
So have a look at the websites, inquire at AAA and come back for reviews of attractions you are interested in.