The caves of South Dakota are located in the Black Hills a hilly landscape around Mt. Rushmore. The name of this area comes from the dark forest of conifers. The most famous tourist attraction, Mt. Rushmore Monument, shows the geological structure of this area: the central granite core.
The Pahasapa limestone was created during the Mississippian period, approximately 360 to 330 million years ago. A first karst system developed in this undisturbed layers which was later buried by younger sediments. Into this layers the central Black Hills granite intruded from below, 60 to 40 million years ago. The granite intrusion, lava coming from the upper mantle broke through Pahasapa limestone, but didin't reach the surface.
Inside the rocks it took very long to cool down. During this time the ground water in the limestone was continually heated by the intrusion and was so able to dissolve and transport several minerals from the granite into other rocks. This minerals were transported into cracks forming ore veins.
In the limestone the dissolving process renewed and a second stage of cave building occured. It was during this era that the caves, as we now know them, developed. But this time, the karst processes only took place in a rather small ring around the intrusion. Outside, the limestone is still deeper and filled with groundwater, and the central area consists of granite, which is not soluble.
So all the caves of South Dakota are located in this ring of limestone, and all their passages run along lines that radiate outward from the approximate center of the Black Hills near Harney Peak.