I live in central New York State, and have never been to Connecticut, and with the comments here, I'll not be going ever. About the only thing I had wanted to visit was Mystic Seaport, but I can visit it in my next life...maybe.
Eastern, CT is actually quite pretty. Mystic and the areas east into RI along the shore. North up to the Mass line is actually fairly rural. You also have Foxwoods and Mohegan Sun casinos there. These are two of the nicer casino complexes in the country. Imagine Turning Stone, but much bigger and more to do with multiple golf courses and 30+ restaurants to choose from. Mohegan Sun has an arena that seats 8000 people. Foxwoods is the largest casino in the world.
The rest of CT sucks unless you are one of the mega rich people who live in Greenwich where a fixer upper starts at $1.5 million. Estates go for $20+ million. Old Money and Wall Street hedge fund types.