Interesting area. I vaguely looked at caving when we honeymooned there in '95 but I didn't pursue it, so can only give general touristy comments! From what I recall, shorts, tee shirts, cotton boiler suits and kneepads would be the appropriate clothing for many SD caves.
Deadwood is well worth a look around; the most sympathetically restored old buildings are mostly casinos now but you can wander in and out at will and without charge to admire the recreated decor.
Lead is still a genuine metal mining town and worth a drive through; there's a view point into the opencast - numerous old levels and stopes can be seen in the pit walls.
The Badlands are half a day's drive from Deadwood. Its a bizarre landscape and well worth seeing. There are only a few short trails as the ground is mostly slippery clay. What was signposted from the national park building as the most challenging trail was only around a mile of easy (though slippery) walking but did gain sufficient height to provide very photogenic views from a 'window' like feature part way up a face.
Harney Peak, the highest peak in the state, and the highest point in the US east of the Rockies is a pleasant two hour walk each way from a car park in a road pass to the abandoned stone-built fire tower on the summit (about 8,500ft from memory). We did it in 18in of spring snow and really enjoyed it; there was a mild scramble up the final peak for, say, 50ft. Excellent views from the tower of numerous granite ridges and forests.
Mt.Rushmore was a disappointment as the visitor centre is a mile or more from the sculpture and from the sole viewpoint (there are lots of trees) it looks less impressive than in postcards because you are a mile away and all the postcards were taken using long telephoto lenses.
Enjoy yourselves!
