What should we add to the visit?

Mt Rushmore and Crazy Horse and Custer State Park are in close Proximity. As well as Needles Highway Scenic Overlook. Rushmore Cave tour is great. Bear Butte State Park is Sacred Space. Sturgis (South Dakota) and the Badlands National Park. The Black Hills. It is the best state to drive through. You can stay at Cheyenne River Motel in Eagle Butte. Right in the middle of the Cheyenne River Reservation.

Crazy Horse Memorial.  It's nowhere near finished, and likely never will be, but it's several times the size of Mt Rushmore, and the interpretive centre explaining the history of the Native American peoples in the region is huge, very informative and enlightening.  

Downtown Rapid City also features life-size sculptures of all the U.S. Presidents at the corners of major intersections.  All Presidents through George W. Bush are represented, and Obama's sculpture should be unveiled sometime in early 2019.  It was fascinating how short Madison, Van Buren and Benjamin Harrison were, and how huge FDR's hands and feet were.  There is an interpretive centre where you can pick up a map showing which President is where.

Museum of the American Bison (1251 Ave of the Chiefs, Custer SD) in the town of Custer, which is where the movie "Dances With Wolves" was filmed is a small but worthwhile attraction if you can tune out the left-wing Hollywood liberal guilt trip and focus on the bison and the relationship between them and the Native Americans who depended on them.  [The museum was built and paid for by Kevin Costner.]  The surrounding grassland has been restored to how the Native Americans would have found it, and there are walking trails.  

Cathedral Spires Trailhead is a great 4-5 mile hike of easy-moderate difficulty. Rankin Ridge Trail is a shorter and less strenuous, but good hike.

Tally's Silver Spoon, a trendy upscale place in downtown Rapid City serving creative and gussied-up traditional diner fare, is the best restaurant in town.  I'd recommend staying at the historic The Hotel Alex Johnson, an Ascend Collection hotel, also in downtown Rapid City.  Book a low floor so you can use the stairs, because there are only 2 elevators and they're sloooooooooooooooooooooooooooow.

Lots of possibilities, so you'll have to filter based on your personal travel preferences:

Crazy Horse - private, so more expensive, but well done

Custer State Park - check the map of the buffalo first, otherwise you might miss them

Badlands National Park - if you are active

Laura Ingalls Wilder Homested Site

Corn Palace

Needles Eye Tunnel - hiking

Legion Lake - canoeing

Evans Plunge Mineral Springs - natural hot springs pool

Mammoth Site - paleontological excavation site

If you’re ok with being underground, give Jewel Cave National Monument or Wind Cave National Park a try. We’ve been only to Jewel Cave so cannot speak for the experience at Wind Cave but found the ranger-led tour of Jewel Cave to be outstanding. It was not strenuous, and there were people of all ages on the tour. You have an opportunity to back out before you go too far into the cave in case you’re feeling uneasy, and if you feel ok you‘ll have a unique experience inside a natural wonder.

Another idea is Mount Moriah Cemetery in Deadwood. It has the graves of Wild Bill Hickok and Calamity Jane and sections for the Chinese and Jewish communities. It was peaceful and beautiful.