The trails at Chickasaw Trace Park are undoubtedly the best bike trails anywhere near Columbia, Tennessee. There are a ton of trail signs out on the trails to indicate what directions you should ride, which trails are expert/intermediate/beginner, and maps to let you know where you are.
The trails are popular for expert riders and beginners alike. The man-made features on the paths are well-kept and a good challenge for any rider. Be aware that the lengthy "Trail of Tears" path is the most difficult trail in the park; there are plenty of entrances and exits for that trail section, though.