Our favorite part of this beautiful state is the portion around the old lead mines and Mark Twain Forrest south and west of Desloge. Just take I-55 south from St. Louis then hit Hwy. 67 south.
St. Joe State Park near Park Hills or St. Francois SP north of there are both acceptable parks. There is also Johnson Shut-Ins SP a little further south. You might also consider
Big Creek RV Park.
In that area you have Taum Saulk Mountain (highest point in Missouri),
Ft. Davidson SHS,
Elephant Rocks SP,
Missouri Mines, and the very nice
Arcadia Valley.
On your way south to US 60 to head towards Springfield, a stop in the
Ozark Scenic Rivers area for a cool float trip or wade in the rivers would be a nice break.
There are many scenic roads in the area to enjoy also. Not knowing what you like it is difficult to recommend things but to us this area is the essence of Missouri.