Cycling is pretty popular around here. You will find most folks riding south of Nashville. If you're just visiting and need a place to ride for a day or two, then I'm with the previous poster and recommend the Natchez Trace.
If you are near downtown, stop in Cumberland Transit on West End and they'll point you in the right direction.
www.cumberlandtransit.com
Other good sources-
http://www.harpethbikeclub.com/
www.nashvillecyclist.com