Audubon Acres, a 130-acre preserve located 13 miles east of downtown Chattanooga, is a good spot for some trail running. There are 5 miles of trails along a creek South Chickamauga Creek and through woods, on a loose sandy soil surface. The trails are easier and flatter on the Visitor Center side of the creek, and hillier and  a little more rugged on the other side. See this page for some suggested routes. One issue of runners here is that the trails are short and interconnected, so to put together a longer run you’ll have to do some overlaps and repeats.