Start at the dam below woodsville nh and paddle to Hanover nh

Having done the entire river (see https://www.ctriver.org/connecticut-river-kayak-adventure/ for details), I recommend as far north as you can make work. The river was faster and the wildlife more plentiful. There are a number of nice primitive campsites for river users. Most of the put in spots (like Canaan, VT) had ample parking. Watch out for reservoirs/dams; no river flow in the reservoirs and some of the portages are challenging. Hope this helps.

We did three days last year and camped. We started at the Bloomfield VT access (Debanville landing) there was a nice spot to put in where we accessed the river by crossing someone's field (there were tracks and a parked car belonging to two anglers there so we just drove down and unloaded there) but the water was quick right were we put in. There was another put in location just up the road with very limited parking but there was a camping spot there, and even a store within walking distance to even get a pizza! We did 5 miles the first day since we started late in the day (@430) and our companions had a mishap with their canoe and needed to dry out there gear! We found a spot along the river big enough for two tents and camped the evening. Day two we did 14.7 miles we passed the Benton campground I think in this stretch and it was very nice. Port a let, picnic table etc. At one point we passed an area that appeared to be a campsite but you literally climbed up a ladder on the bank. We didn't stop here. There were plenty of long, wide sandy beaches in the part of the river were you could stop and swim or camp too. Our last day was short (planned due to weather) and we did the final few miles and got out at Wyoming dam. The Portage here was a narrow rocky goat path to get up a hill. Doable but a surprise. Putting in after the dam looked like a much easier task, although we only walked down for curiosity and were not putting back in for the day. We went July 20-22 2018 and had this stretch of river to ourselves, aside from the bear, beaver,otters and multitude of various birds. We had one dog with us, no kids this time, 2 kayaks and a canoe. It was a wonderful trip. Looking forward to another stretch this summer. I did use two apps on my phone to help us navigate between points (campsites etc) and as a new kayak found it very helpful to be able to know what was nearby to keep an eye out for.

See my recent trip report here http://www.connecticutriverpaddlerstrail.org/crpt7/node/7169

We did this trip in four days but you could start further north and still avoid portages stretching the trip to a week. The Pastures Campground was really nice and well worth the $25 per night. The showers and bathroom facilities were very clean and the sites were large. Just start planning at Kilowatt Park and go up river on the map as far as you can to the next dam for your planning. The actual trip will, of course, be downriver. No portages and a fun trip.

It looks like you could put in at the Comerford Dam (River mile 283) and go all the way down to Kilowatt Park (River Mile 219).