Ohio suffers a misconception of having nothing but straight roads. Certainly in the northern part of the state where modernization and development have straightened roads to reduce travel time and increase safety, this hold true.
South of route 30, the Old Lincoln Highway, roads have not been rerouted. The roads in southeast Ohio were plotted long ago. These roads were built around streams and hillsides and remain with paths unaltered. This means great curves and changes in elevation all within a days drive. There are lots of places to stop and stretch your legs.
I suggest you do not take a map. Just load up the family and friends, roll the windows and top down. Wander around the countryside with no agenda other than stopping to enjoy the food and sights. Be safe and enjoy!