Although that part of the country wouldn't be my first choice for a tour, there are a few areas and rides you might want to consider. One is the Natchez Trace Parkway, a 710 km route from Nashville, Tennessee, to Natchez, Mississippi.

http://www.nps.gov/natr/index.htm

Many states have organized rides each year. The oldest and one of the best is called RAGBRAI, which crosses the state of Iowa from west to east every year during the last week of July. There are thousands of riders each year and it is very well organized and very inexpensive.

I hope you are aware that the Mississippi valley and southeastern US are extremely hot and humid in the summer. It is very different from the weather you are accustomed to in the Netherlands.

By the way, the Great Smoky Mountains are in eastern Tennessee and western North Carolina, not in Kentucky as you were told above.