Within a few miles west of Medicine Lodge on US Highway 160, the terrain begins to get more uneven and you see a sign pointing to the Gyp Hills Scenic Drive. It's a short, but pleasant drive through some scenic ranch land. Not too far to the south, Ted Turner owns a large spread on which he raises buffalo.
If you stay on 160 to the west as far as Coldwater, Kansas, you will drive through some pretty rough country, rocky with lots of cacti. It looks more like New Mexico than Kansas.
Frankly, just about everything in this part of the world is off the beaten path. The Guinness Book of World Records claims that the countryside outside Medicine Lodge is one of the quietest places on earth! If the wind ever quit blowing and birds stopped singing, then I see how that could be true...
The highway cutting through this countryside gives you a good impression of the local scenery, which is quite unique. You'll spot features like the Twin Buttes and the Flowerpot Mound which can be enjoyed from several scenic overlooks. There is also a backroads scenic drive along gravel lanes that takes you deeper into this land of red soil, pink crystals and green cedar shrubs.
In particular I suggest veering north off the highway, aiming for Sun City and Belividere, parts of which are open rangeland.