Jane, it's going to take you a little while to get to East TN staying two days at each place as you are 1,000 miles away. But, that's OK. :)
I'll list a few parks along the way that we have stayed in many times. I go from TN to CA quite often from Memphis, TN.
Mustang Run just west of Oklahoma City is very nice and just right off of the interstate. But, thats only 112 miles from Elk City.
Ivy's Cove in Russellville, AR. It's also right off of I-40.
Do not stay........KOA North... Little Rock, AR. Warning..... IT IS NOT BIG RIG FRIENDLY!
Tom Sawyer RV Park, West Memphis, AR. (Memphis, TN). Nice park on the Mississippi River. The neighborhood getting there is a little sketchy but once you get there, it's very nice.
Parker's Crossroad RV Park, Yuma, TN (Lexington, TN) exit 108. Nice campground.
Nashville area.... KOA, Music Vally Dr., expensive but near a lot of entertainment and restaurants. KOA, Lebannon, TN, on the east side of Nashville, its a good stop but always full.
On Music Valley Dr., there is a Yogi Bear RV Park and Two Rivers campground.
Crossville, TN, KOA is nice but the whole parks slants.... couldn't get completely level but nice concrete pads.
Crossville, TN, Spring Lake RV resort is very nice too.
Kingston, TN, Soaring Eagle is a nice stop, just stayed there recently on the way back from NC.
Some of these parks may not be the perfect stop 'time or mileage' -wise, but I've been to them and would return again.
Good luck, safe travels,
MM.