There are numerous trails and hiking areas in the Ozarks for you to enjoy..
Half way between Springfield and Branson is Busiek State Park, where hiking can take as little or as much time as you'd like. While you are there be sure to visit the National Tiger Sanctuary (open Wed - Sunday for guided tours).
Another beautiful area to hike, bike, or rent ATVs is Dogwood Canyon, down Highway 13 south of Table Rock Lake.
And Talking Rocks Cavern, just west of Branson, introduces you to caving among stalactites, stalagmites and other amazing rock formations.