Im from Independence, MO so right in your neck of the woods, and have done the drive probably 6 times or so. (we were married at WDW in Jan 2002 right after 9/11 so with dresses and everything else driving was the only option!). Last time was just five months ago. We have stopped in a lot of different places.
When we leave in the evening around 4pm or so we stop in Mt Vernon, IL, its about 6 hrs out, and we usually get there about 11PM. Several good, mid-level options there, and its a nice safe little town. (I 64 and I 57)
Last time we stopped in Murfreesboro, just south of Nashville off I-24, room rates are a lot more affordable then nashville, TN. Usually I work 1/2 day and we get there about 11PM. There is a Comfort Suites there that we stayed it, it was fairly new and customer service was great.
Last place we have stayed in Valdosta, GA off I-75. Only try to get to Valdosta if you leave early in the morning, otherwise you won't get there into the wee hours of the morning (from experience). DONT UNDERESTIMATE GEORGIA ITS A FOREVER STATE. Like you drive into it, and its FOREVER until you get out of it. However if you can get there, its a short drive to WDW then next morning.
Macon, GA isn't a bad idea either, its about 2 hrs north of Valdosta, so its a little bit more doable. I've looked into before, but we have never stopped there.
Couple other tips. Whatever you do, no matter how great an idea it sounds... NEVER EVER EVER TRY TO DO THE DRIVE IN ONE DAY. My husband tried to do that on the way back once. It was insane. We stopped outside of Columbia, MO at 3AM, we were just to tired.
If you can try to stop at the Paducah, KY Rest Stop, its really neat old mansion, and not your boring run of the mill rest stop.
I mentioned I-75 through Georgia right, how it goes on forever? You have been warned.
Let me know if you have any questions. The drive is definitely an experience. Lots of fun little things to see along the way, If you stop at Ruby Falls let me know if its worth it, I have seen the sign atleast a dozen times... and never stopped. I love the fireworks stores along the TN/GA border, at night you can't miss them. They have about as much neon as Las Vegas.
Jennifer