The Natchez Trace is probably the most popular Biking road in this area. I've never biked it, seeing as I have no bike yet, but I have driven it many times and it is a very beautiful part of this country.
Subject:RE: 6 Day Bike Tour.. Jackson to Nashville
I have never biked the whole route but a few sections. Yeah, its a great road. Very scenic and no heavy trucks/commercial vehicles allowed make it great. Also I believe their is only a 50 mph speed limit to further make it cycling friendly. The only thing I remember not liking was that there practically no shoulder on the road.