A few observation about my time in CT.
New England is small. Draw a 250mi arc around Meridan and you can pretty much throw a sheet over the place.
There is a lot of really cool things to do, with or without the family. On the weekends I couldn't make it back to Maryland during my three years at Sikorsky, I had fun exploring New England: Mount Washington, Saratoga Springs, West Point, Bridgeport Ferry to LI, etc., etc.
Nice minor league baseball in the area. I used to go watch the New Haven Ravens but they are disbanded. Looks like Bridgeport now has a team.
Costs money to go to go to the beach, parks, etc. You need a town pass or purchase a day pass.
Connecticut (CT) Beaches, ocean beaches, lakes & ponds, fresh water swimming, salt water swimming
Get EZ Pass for tolls. You do not want to be without it, 99% of the time you'll save wait time at the toll booths with EZ Pass. Driving in many parts of New England costs a lot of money.
There are really great roads in the area. When I knew I was going to be staying for the weekend, I always drove up in 1983 SC.
Enjoy. One year you and the family can do easy with a little planning. I did it pre internet so with all the communication options for staying connected you will be fine.
All the best. DC isn't too far for a road trip