The Ozark Mountains are in northwest Arkansas. The southern half of Missouri (south of I-70) enjoys valleys cut into the Ozark Plateau. It is all interesting, but I've traversed the Ozark Plateau hundreds of times over the past 35 years, gone through the Ozark Mountains only a few dozen times, on a half dozen different routes. Anything north of I-40, west of US-65 is worth visiting on into the eastern fringe of the Ozarks in Oklahoma, east of US-59.
The real find, however, is in the Ouachita Mountians, one of our oldest mountain cores, south of I-40 between Hot Springs, Arkansas and Talahina, Oklahoma. There are no good north-south routes, the trend of the mountains is east-west, but once you break out of the mountains it is all Oklahoma lake country going north to Kansas.
North of I-40, well into northern Arkansas and NE Oklahoma, you will be in the navigation management area of the Arkansas River system, which means there are nearly a hundred Army Corps of Engineers managed reservoirs and lock and dam systems, most of which have low-fee or no-fee recreation access areas. I do most of my camping in COE recreational access areas, or state parks where the state has taken over management of a facility on a Corps reservoir. This all stretches into north central Oklahoma, southeast Kansas and south-central Kansas.
Once you get into Kansas, almost every county has a county fishing lake, at which you can camp (usually no-fee), but there may be no facilities other than a pit toilet somewhere around the lake. There are also town lakes, with more or less facilities, but not always camping.