We stayed at Table Rock Lake State Park last summer. You wouldn't know you were near Branson. There is a nice paved trail from the marina to the visitor center.
Roaring River State Park in SW Missouri (Cassville) is real nice although trout season ends in October and it is very busy that last weekend of season. Fishing is allowed on the campground 3 side of the river. Bull Shoals Lake SP on the white river below the dam is nice and Buffalo Point campground on the Buffalo River has beautiful bluffs. Scenic route 7 is beautiful.