If your schedule permits, consider driving east on the Interstate from Rapid City to Badlands National Park (about an hour). Not only is the landscape beautiful in a way, but the kids are permitted to climb around certain areas. We've been there several times, and when our kids were young teens they couldn't wait to get out and scramble over the hills. Additionally, you may spot different kinds of animals as you drive along the park. And when you exit, you will be very near Wall, home to Wall Drug. As noted in an earlier post, the Buffalo Bill museum in Cody is first-rate and is affiliated with the Smithsonian. I think the kids will enjoy that as well. Finally, nothing beats seeing the critters in Yellowstone in their habitat. Remember, they live there and are only letting you visit. By the way, it can snow any month in Yellowstone and nothing beats the year my kids built a snowman in late June.
Bob