My ventures through Texas were on I-40 stopping at Amarillo on the way to the Grand Canyon, Then Roswell, NM / Lubbock / Dallas / to Shreveport, LA, and last year Nashville, Memphis, Shreveport, Luling, TX to Beaumont, TX back North.
I remember I-40 in Texas as rolling hills the rest was no problem. I-20 was no problem traffic heavy around DFW area. In Nashville, We stayed at the Two Rivers RV Park (KOA, Jellystone and Two Rivers are next to each other) close to the Grand Ole Opry and 15 minutes to downtown. Nice Campground second time there will stay there again. Running the numbers about half way between Abilene, TX (taking that as Central TX) and Nashville is Arkadelphia (AR) Campground at about the 420 mile mark while Nashvills is 835 miles. Has decent GS numbers haven't stayed there yet but looks OK. Last year on the way back from Beaumont we went to Pigeon Forge, TN and visited Gatlinburg, TN. It was mid-August and was a Sat-Mon stay. The place was like a zoo, Lines everywhere and grid lock on the roads. We ended up skipping the shows, restaurants etc. and drove around the Smokey Mountains NP for the two days. Good bit of traffic in the park but not bad. From what we could see it looked like a nice area and we probably will return during the shoulder season when we get a chance.
Other recommendations if your stops change - I stayed at the Downtown Riverside RV park in Little Rock,AR - A municipal park nothing more than a parking lot with hookups but right on the Mississippi. Thought it wasn't bad for a overnight stop. Memphis stayed across the river in West Memphis, AR at the Tom Sawyer RV Park on the flood plain of the Mississippi. Nice place if isn't flooded. clean quiet place a quick 20 minutes to town.