I went on a white water rafting day trip many years ago on the Penobscot. It's a very nice area, but unfortunately, I haven't been able to make it back there since.
Another area I would recommend would be the Saco River. My friends and I used to canoe down a 13 mile stretch of it over the course of 2 days, staying overnight on a section of beach along the river. That was a fun time, and sounds similar to what you're describing. We used to rent canoes from a company in Fryeburg, ME, which dropped us off and picked us up at the end of the trip. I want to say that we got the canoes from either
Saco River Canoe & Kayak or
Saco Canoe & Kayak.