Our Catoosa trip was quite interesting. We'd never been there before and had no plans other than find the Nemo Bridge and some fun trails to ride.
First off some directions: From Oak Ridge we followed 62 through Oliver Springs all the way to Wartburg. We went straight through the red light and made a right on Main Street. Following Main we turned left on Maiden Street then right on Spring Street. That road turns into the winding Catoosa Road and will take you to the old Nemo Bridge. (Shown at left)
After crossing the bridge we continued on up the hill and eventually came to this sign and a T intersection. Flipping a coin resulted in us heading right at the T. We then found a sign with some rules stating, among other things, that the park closes at dark and visitors aren't allowed during big game hunts.
It's recommended that you stop by or call the National Park Service Visitor Center in Wartburg before you head up there to make sure it's open. They are at 208 North Maiden Street and their phone number is 423-346-6294.