How About the Grand Ronde?
Grand Ronde, in Northeastern Oregon. There's a great stretch from Minam Store to Powwatka Bridge, or farther, if you like. You can rent boats at the put-in. Beautiful, lush, scenery, mellow whitewater, lovely campsites, mountain goats. No permit lottery - just self-register at the put-in. It's a perfect family trip, in my opinion.