I was in the Black Hills last June during a cross-country move. It is a beautiful area and I wish I had more than three days to spend in S.D. The Black Hills reminded me a lot of the lower Sierra's, covered with pines and small alpine lakes. We camped in the Badlands, and at Horse Thief Lake just west of Mt. Rushmore.
The photo opportunities at Mt. Rushmore are somewhat limited by restrictions on where you can hike. Early morning provides the best light on the sculpture. There is a night time colored light display/program if you are interested in that sort of thing. The Crazy Horse monument close by is as impressive as Mt. Rushmore.
Nearby is the north entrance to Custer State Park which contains several gorgeous small lakes (Sylvan Lake is very pretty and has some interesting rock formations) and large expanses of grasslands with Bison. It is a little late in the year to see the lush prairie grasslands, but they will still be photogenic.
Although we did not have time to visit any of the caverns, but your son would probably like Wind Cave National Park and Jewel Cave National Monument in that area. Wind Cave NP is also home to large expanses of prairie and bison. My son (age 12) is still begging to return to the town of Keystone (very near Mt. Rushmore) because there is a ski lift/bobsled type attraction. It was closed when we were there for maintenance but looked like it would be fun diversion from the scenery.
The Badlands are a few hours away, a must see if you have a couple of extra days. Devils Tower NM is a short distance off the main highway between the Badlands and the Black Hills. Spearfish canyon on the North side of the Black Hills was a disapointment that time of year, but your mileage may vary. There were several old gold mines with tours in Lead and Deadwood near Spearfish Canyon that your son might like.
I really want to go back to S.D. in the April-May and spend at least a week tramping around. The landscapes and skies are big and beautiful. Have a great trip!
Black Hill Forest map link: http://www.fs.fed.us/r2....est.jpg