Check the Asheville Visitors Center web site. They have list of day trips centered from there. One or two feature waterfalls on the route. There are many in the area.
Cuiver River SP campground in Troy, MO. This is off of I-70 near St. Louis. This is a nice state park about 15 miles from the interstate. Nice and quiet.
Wilson Lake in Kansas has Sylvan Park just below the dam. Beautiful old trees (lots of shade) and very quiet. Exit 206 on I-70 and north about 5 miles on the right just before the dam (turn as if for road 181).
If you stop at Wilson Lake, go on into Lucas, KS. Brandt's meat market in downtown is the place for pepper sausage, pepperoni, and jerky. A stop at the Garden of Eden and the Grassroots Art Center is also worth the time. The K-18 diner has good food and is reasonably priced.
8 kids (5 still traveling)
1 darling wife (won't leave home without her)
Ford E-350 SD V10 Van
Jayco Eagle TT
Hensley Arrow
You may want to check out the Vallecito Lake, Colorados best kept secret when in the Mesa Verde NP area. IF you Google it you will find lots of info also the Bayfield Co CC. On your return you have a empty space from the Ozarks to Tucson. Check out DodgeCity KS. Palo Duro Canyon in Amarillo TX. It is the second biggest canyon. Carlsbad caverns NM. Lincoln County NM ( Billy the Kid) country, White Sands NM National Monument, and the VLA Very Large Array West of Soccoro NM. Have a great trip.
On return trip I recommend coming back from Smokey mts to North Arkansas (OZARKS)Come and camp for a night or two at Blanchard Springs Caverns. Campground on Sylamore Creek with Clear Shallow water flowing through several camp areas and The 4 y/o will love going down into the Caverns. I am taking my 5 y/o Granddaughter there for a few days to camp and see the caves. She is very excited. You will probably see some of the Buffalo National River on your way through also.