Its pretty easy to spend a week while outdoors the majority of the time in the Black Hills. So much to see, so much to hike or rent bikes. Neat communities to spend time in and places to stop and see. Hit the Badlands, the Mammoth Site at Hot Springs, Wind Cave, Custer State Park, hike to Black Elk Peak from Sylvan Lake, drive the Needles Highway, Rushmore, tour a mine, hike Spearfish Canyon and check out some waterfalls, fish for trout, ride some horses, go to Devils Tower and the Vore Buffalo Jump in WY, Deadwood has great entertainment, Bear Country, Tetonka, Red Ass Winery in Hill City, the list is endless. We have done this two times as a family doing a VRBO since there was so much to see and do. I had hunted out there several times prior for turkeys so knew my way around real well.
We are taking my 12 year old son out of school in Sept to hit Yellowstone and the Tetons during a slower tourist time and enjoy the elk rut. If you do head out that way through the Bighorns stop at the Medicine Wheel. There are also some neat petroglyphs west of Thermopolis. If you come home through Eastern WY you can follow the Platte and some historical sites from the Oregon Trail.