There’s Excitement in Those Beautiful Black Hills of South Dakota : Grasslands and Mt. Rushmore were less than thrilling for these children. But they perked up exploring caves and seeing herds of bison.

“Let me know when you see a buffalo,” Matt said, not believing we’d ever spot one outside a TV set. He was engrossed in his Game Boy in the back seat--too busy, he said, to watch boring Black Hills scenery through the minivan windows. That changed in a hurry.

“Look!” Reggie said excitedly, pointing to the side of the road where a huge, furry brown bison--that’s the correct name for the 2,000-pound animal--was nonchalantly grazing. A few miles further, we slowed down to let another lumber across in front of the car. Custer State Park, where we were driving, has one of the largest bison herds in the world: 1,400 in the 73,000-acre park.

The Game Boy was forgotten. The kids were so involved looking for wildlife they forgot to fight. Before we pulled into the Mt. Rushmore parking lot, we had spotted antelope, bighorn sheep, mule deer and rabbits, as well as more bison.

The wildlife, I confess, were a lot more exciting to the kids than Mt. Rushmore National Monument, stunning though it is with its 60-foot-high sculptures of George Washington, Thomas Jefferson, Abraham Lincoln and Theodore Roosevelt, jutting out of the mountaintop. I did my best, explaining the sheer magnitude of the accomplishment of sculptor John Gutzon Borglum, who devoted the last 14 years of his life to the project. One eye is 11 feet wide; a nose is 20 feet long.

We visited the sculptor’s studio and I told the kids why these Presidents had been chosen: Washington to represent the birth of the Republic; Jefferson for the idea of representative government; Lincoln to represent our permanent union and equality for all, and Theodore Roosevelt for the 20th-Century role of the United States in world affairs.

“You mean we can’t climb up to the top?” they said in shocked disappointment. They were more interested in getting back to the parking lot to see how many different license plates they could find: Most states were represented on the summer evening we visited.

There’s no doubt that Mt. Rushmore--work stopped soon after Borglum’s death in 1941--remains the most famous site in the Black Hills, and one of the best-known tourist attractions in the country, drawing 2 million visitors a year. Many vacationers on their way to Yellowstone make it their only stop. But they’re missing a lot--especially if they’re traveling with children. The Black Hills area of South Dakota also contains long, spooky caves; the site in Hot Springs, S.D., where more than 100 prehistoric mammoths perished; the rich fossil deposits; the rugged countryside of Badlands National Park, and Deadwood, the historic gold-rush village that looks like a town from Wild West days.

We lingered for a couple of days, staying in a cozy cabin with a fireplace in Custer State Park, the second-largest state park in the country, and wished we’d had more time. (Call 800-658-3530 for reservations.) This is, of course, “Dances With Wolves” country, Kevin Costner’s Academy Award-winning epic film. More than 50,000 American Indians still live in South Dakota, and it is a wonderful place to teach children about their history and culture.

One good place to start is 17 miles southwest of Mt. Rushmore at the Crazy Horse Mountain Memorial, the largest sculptural undertaking of its kind ever. Keep in mind that the Crazy Horse memorial is not a government project. The sculpture is financed primarily by admission fees ($12 a carload) and the efforts of the family of the late sculptor Korczak Ziolkowski, who dedicated more than 30 years to the project.

When finished, the carving of Chief Crazy Horse will be 563 feet high, 641 feet long: All four heads at Mt. Rushmore would fit inside Crazy Horse’s head. (If you come in early June, you can join the thousands who gather here for the once-a-year chance to climb the 600-foot mountain to view the progress close up. (Call 605-673-4681 for more information.)

We saw workmen up on the mountain, though they weren’t blasting the day we were there. There is also the impressive Indian Museum of North America at the base of the sculpture, showcasing some 20,000 artifacts from the region--rugs, dresses, jewelry, weapons--even toys and a tepee.

The kids were impressed with the hands-on area where they could grind corn, feel pelts and go inside a lodge. Being able to take home a piece of the rock seemed to mitigate their dismay at once again not being able to climb the mountain.

That’s one reason why they were so thrilled when they got the chance to explore Wind Cave, one of the world’s longest with more than 53 miles of mapped passageways. (Call 605-745-4600.) Nearby Jewel Cave, also one of the world’s longest, is known for its unusual crystal formations (call 605-673-2288).

There are wonderful ranger-led candlelight and spelunking tours available at Wind Cave, but because we had 2-year-old Melanie in tow, we opted for a more conventional tour that took us half a mile inside to see the world’s best examples of boxwork, thin veins of calcite that crisscross the walls in a honeycomb pattern. The kids were especially impressed when the ranger turned out all of the lights to give us a sense of what it had been like for the early cave explorers.

Early the next morning, we headed off on a different kind of adventure with retired Marine officer Joe Weston: a two-hour Jeep tour into the back country of Custer State Park. It was a bargain at $12 for the kids and $15 for us; kids under 3 are free. The Buffalo Jeep Safaris (tel. 605- 255-4541) begin in May and run through September. The first week of October they will have a buffalo roundup: Riders will herd all of the bison to one place to be branded, vaccinated and sorted. It will be open to the public. We watched scores of bison grazing with their calves, imagining what it must have been like when thousands of the beasts roamed the plains.

A few miles later, friendly wild burros surrounded us, begging for handouts. They loved our Cheerios.

Taking the Kids invites reader questions and comments about family travel. Address them to: Taking the Kids, 2859 Central St., Box 119, Evanston, Ill. 60201.