If I was doing a road trip for a day there, I would climb up Big Red and take Parts Unknown over to the Cottontail descent. Afterwards, climb the most direct way back up and ride White Oak Ridge from south to north. Finally, pedal the most direct way to the Flow Trail (Nutty Buddy) and do as many repeats as your legs and heart desire. There are several more miles of well built trails that you can add on if you just want a good xc workout, but they are mostly forgettable in terms of features or elevation.
The trails are well marked and there is a map at the trailhead in case you don’t have Trailforks.
Edit: Also check the weather for rain and freeze/thaw as Chattanooga area trails don’t ride well in the wet.
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