The Klamath River is a very long river starting in south central Oregon and entering the Pacific Ocean at the town of Klamath in north west Caifornia.
If you end your trip in Oregon there is a train station in Klamath Falls that will take you to Eugene or Portland, Oregon. If you end it in Klamath, California, rent a car and drive to an airport in California or Oregon.
My wife and I had a family emergency while rididng down the Pacific when we were a short distance north of Klamath, California. It required us to get home as soon as possible. We rented a car in Klamath and drove home to Oregon. It was pretty reasonable.