Are you just visiting, doing the tourist thing, or looking for a seasonal?
Most campgrounds in Connecticut are in the East and Northeast parts of the state. Pretty much everything
in Connecticut is within 50 miles of Hartford, just that sometimes there isn't a direct highway route.
A very nice campground relatively close to Hartford is Nelson's Family Campground, 71 Mott Hill Road, East Hampton, CT 06424. A little farther southwest, and in a beautiful part of the state, is Wolf's Den Family Campground, 256 Town Street, East Haddam, CT 06423 (Actually, I think both of these campgrounds are owned by the same people).
This map: http://www.epgsoft.com/CampgroundMap/
Is pretty good to get an idea of campground locations, and gives links back to RVParkreviews for reviews.
At any campground, make sure you ask for a full hookup site with sewer, and be aware that with holiday weekends and/or last minute reservations the full hookup sites may already be reserved.
Keep in mind that most Connecticut State Parks do not have electric, water, or sewer hookups -they are primarily dry camping.
Hope this helps!