About an hour and a half to the northwest is Devil's Tower. Located in the Bear Mountains of Wyoming, this is really the northern extension of the Black Hills. Made famous by the movie Close Encounters of the Third Kind, the tower is a natural monument that attracts climbers from around the world. It's not uncommon to find someone from New Zealand, England, or India working their way up the vertical flutes.
See my Devil's Tower tips
East on I-90 is Badlands National Park. Best known for being blazing hot, it is the home of fossils from the Cenozoic era (that the large mammals, after the dinosaurs died off). It is a broken rugged line of cliffs facing south into the Sioux Reservation. Here the buffalo still roam and prairie dogs have colonies tucked away in the grasslands.
See my Badlands National Park tips.
Highway 16 connects Rapid City to the Black Hills area, and there are many little tourist attractions along this road near the city. I remember a human maze that was never open when I was there. There are many places selling 'Black Hills Gold,' and the little trinkets are cute enough to be one of several Christmas gifts for family members. I also remember a couple of putt-putt places there. I played one of them one night on my way back to Hill City from having to replace something that had broken. It was a tough course because it would have been easy if I could putt straight. I can't, so I was all over the place. Still, it was fun.
Camp near Deerfield. Pack your warm clothes, even in summer. Others: drive Nemo Road (not as touristy), swim at Evans Plunge in Hot Springs (huge pool fed by warm spring), go to a rodeo (several to choose from). Picture is of pronghorn seen from the Wildlife Loop in Custer State Park.
Buffaloes and prairie dogs on top and gorgeous caves with stalactites below ground level - that´s Wind Cave National Park. You can take a guided tour through the cave system.