I would urge you to not even consider major routes like US 127. High traffic volumes and minimal shoulders are not what you want. I'm not sure what your needs are either. Not to disagree with Valygrl, but cyclists who will be camping plan different routes than those that need motels every night.
A word of warning - river crossings - the construction of major reservoirs, especially on the Cumberland River, has limited the number of potential crossing points. Not only has this concentrated traffic, but the reservoirs attract a large number of vacationers with boats etc. Ferry crossings are ideal for cyclists. They allow you to experience the river, but they also let the cyclist cross withou worrying about getting run off the bridge and they have very light traffic on the roads leading up to them. Not many left, thought. There are two ferry crossings of the Ohio - one in Augusta, KY and another in the western suburbs of Cincy, OH. There is one ferry crossing of the Cumberland - east of Tompkinsville, KY. Between Burkesville, KY and Williamsburg, KY there are only three crossings - US 127 and US 27 are both dangerous, KY 90 goes east to west.
Most states put out traffic volume maps or tables. There is usually statewide and county data. I would urge you to use the county-level data. You will find the best riding in KY and TN on these secondary roads.
OH -
http://www.dot.state.oh.us/techservs...it/default.htm (interactive)
Ohio county maps must be ordered - not available on line.
KY -
http://transportation.ky.gov/plannin...count_maps.asp
http://transportation.ky.gov/plannin...RS/crsmaps.asp
TN -
http://www.tdot.state.tn.us/projectplanning/adt.asp
http://www.tdot.state.tn.us/Maps/county/default.htm
By using these resources, you can plan a route that has low traffic volumes.
Shoulder width is more difficult. Few secondary roads have significant shoulders.
Even primary highways in these states rarely have shoulders.
Those few roads with shoulders will, most likely, have very high traffic volumes.
Also - HIGHLY RECOMMENDED - the Little Miami Trail from Springfield to Milford, OH - 70 miles.
http://www.dnr.state.oh.us/parks/parks/lilmiami.htm
Feel free to contact me. I've ridden extensively in Kentucky and east Tennessee.
Moderate amount of touring in Ohio, Indiana, and Michigan.
Feel free to contact me.