Named for its awesome caves and miles of underground caverns with wild geology, Wind Cave National Park in South Dakota draws over a million visitors annually. Visit prairies and forests and watch for wildlife like deer, prairie dogs, elk, coyotes and bison (you can't miss them), amidst one of the world's oldest caves, and the first cave to be named a national park.
Wind Cave is a beautiful park to drive through, so pack a picnic and take your time. Camp at Elk Mountain Campground or in nearby Custer State Park. Hikes here are pretty short, so if you want to stretch your legs and get your heart rate up, try out the nearby Black Elk Peak/Harney Peak Trail, or the much easier Lover's Leap Trail loop.
Because it's such a drive for most visitors, don't visit Wind Cave National Park without stopping at Custer State Park, just to the north with incredible rock formations, camping and exploring. Take the opportunity to also drive out to nearby Mount Rushmore National Memorial and south to Oglala National Grassland, and definitely don't miss Badlands National Park just — relatively speaking — down the road to the northeast. If time permits, go gawk at Devils Tower National Monument as well, two hours northwest in neighboring Wyoming (who knew there were so many rad spots in and around South Dakota!).
The park is open year-round, though winters can be cold and summers hot. Here's a great list of the things you'll want to know before you go, including less busy days.
Unlike most national parks, there are no fees to drive through or hike around Wind Cave National Park. There are, however, fees for visiting the caves themselves, which can be found here.
Dogs on leash are only allowed in developed areas of the park, as outlined here.