That would be a bit of a haul. Not sure what kind of trails you are looking for but you have Aetna Mountain (look on youtube, it's famous), Big Fork which is on the back side of Signal Mountain, Lewis Chapel on Flat Top Mountain all about 45 minutes or less from you. If you go towards Marion County you have the cove. There are several spots there each with it's own name but I just grouped them together to simplify things. I'm about 10 minutes outside Chattanooga and know several in Cleveland that I ride with and we try to go at least twice a month.
I got that Jeep thing now it hurts when I pee.