I'm not to familiar with the riding in the Klamath Falls area. There is a lot of forested areas all around the Klamath area, there has be some decent riding in there someplace. I'm sure that you could find somebody to show you around if you stopped at a motorcycle shop. Here is a link that shows some kind of OHV park not to far away in the Keno area. It will also show you some areas around Medford. I have heard there is some good riding above Prospect on Hwy. 62.
If you get up north of Klamath Falls towards Bend (150 miles) there is a lot of good riding to be had. Here is a link that shows you some ideas around the Bend area.