Seldon Neck State Park is a very scenic island located near the river's mouth. Four official campsites (Cedar Camp Area, http://www.connecticutriverpaddlerstrail.org/node/1462 >Hogback Camp Area, Springledge,and Quarry Knob are easily accessible and make for great basecamps from which to explore the river. Consider circumnavigating the island, or paddling up a bay to the town of Lyme. Slow currents make an up and back trip possible - the closest put-in is at Gillette Castle State Park, only 1-2 miles upstream, or the East Haddam Town Landing further upstream. Those seeking a through paddle can take-out at the myriad of access points near Essex, although parking is somewhat limited.
You will need to make reservations atleast two weeks in advance for a campsite, and be prepared for heavy boat traffic in the main channel on sumer weekend.