We make the trip from Northeast Texas to the Lexington area almost every year (I am a graduate of Asbury University just south of Lexington). We have stayed a couple of times at the Kentucky Horse Farm, north of Lexington. It is not so handy for use because of the location clear across the city, but it is a really nice RV park.
We often vary our route by turning up I-55 in West Memphis, AR and going up to I-155 to Dyersburg, TN then connecting through Union City with the Kentucky Parkway system all the way to Lexington.
But to your original question: we have stayed at a little roadside RV park near Jackson, TN called "Joy-O", simple and rural, between Memphis and Nashville. On the other route there are many good campgrounds near the Land Between the Lakes in Kentucky.
Have a nice trip. If I can help with any details send me a PM, I'll be glad to help if I can.