Oh the West Branch Penobscot ... my home run! I lived up there for several summers as a raft guide, but mostly kayaked and lived at the Big Eddy camp ground at the base of the Crib Works. Its a beautiful river in the shadows of Kadadin. Others are right that you should plan to hike up there as well. As for the river, the put in is 45 minutes from Millenocket up logging roads at McKay Station. There is a parking lot right as you turn into the station road. Park there and walk down 2 large hills. At the bottom of the first hill, you can look down into Ripogenous Gorge, which is 90ft below. Walk behind the power station and put in in the eddy above the discharge. If there is no eddy, get back in your car and head up to the dam and you can run a Class V- section called the dry way - no likely though.
There is a river-wide hole to enter the first rapid called Exterminator that you can go right, along the wall, or left around. There is a sweet, catch on the fly, surf wave at the bottom of the big eddy below the rapids after Exterminator. The next mile or so is class III with a few fun play spots. You can scout the Crib on river left taking out not far below the Telos bridge, which is just upstream of the campground. There are 2 entrance chutes you can run, but most take the left chute (Turkey Chute). You can hit the eddy at the bottom left of this chute behind Pillow rock, then ferry across to the island (a fun spot to get out and hang out). This is my most favorite rapid and river, so I'd be happy to share more beta. A few hundred yards past the Crib, you are at Big Eddy and can take out right where you camp.
There is a lot of dead water between the rest of the rapids on the 16 mile section, so you might want to drive to those. Big A is class III with a fast surf wave at the bottom of the 3rd drop. Take out river right after that and walk a few hundred yards back to the put in. It is also worth driving down to Nesaudnahunk Falls to run the drop and play.
If you go in the summer you could run into flows between 2000 and 3600 cfs - depends on how hot it is in Boston and how high the power demand is for AC. 2800 and above gets rowdy fun in the gorge and crib.
I would suggest camping at Big Eddy, so you can take out from the upper gorge-crib section right at your camp site. The camp site is owned by Chewonki (Welcome to Big Eddy
). Stop by in the morning for coffee and delicious baked goods from Susan.
The Kennebec is fun as well, and pretty in its own, but does not compare to gorge-crib on the West Branch. I would not bother with the East Branch. The Rapid River, in western Maine, is also a secret gem. But you need to be ready to follow convoluted logging roads to get there. BC gave other good suggestions and the Seebomoc is super fun as well as Canada Falls, which are upper sections of the West Branch, north of Moose Head Lake and between the Kennebec and Penobscot. Let me know if you want any more beta. When is your trip?