The Natchez Trace is about 15 miles outside of Nashville, TN. It is a scenic parkway and part of the National Park System. For road bicyclists, it offers smooth pavement with low traffic with moderate climbs. I’ve only ever ridden the first 50 miles, but the whole parkway is 440 miles long and terminates in Natchez, MS.
Make sure to take plenty of water and some food with you as there aren’t any stops along the parkway except for a rest area with picnic tables and restrooms. There are areas where you can exit the parkway with access to some small towns, but I haven’t done this, so I can’t comment on what they have or don’t have as far as food or places to stay.