There's more to South Dakota than just visiting Mount Rushmore - and there's lots of ways to save money on a South Dakota vacation. But the most important thing is to plan your trip carefully. Besides saving you money, this will also make sure you arrive when the temperature is comfortable. South Dakota may offer beautiful forests and wonderful museums, but it still gets below freezing in the winter - and above 100 degrees at the peak of the summer!
Mount Rushmore is a must-see destination, of course, and you'll want to leave enough time for the Mount Rushmore visitor center, which features a fascinating exhibit on the creation of the famous monument to four U.S. Presidents. The park itself is free, but it'll cost $10 to park in the parking lot. (If you're really cheap, you can drop off your passengers, and then pick them up later at a pre-arranged time!)
But just 23 miles from Mount Rushmore is the Custer State Park, which is South Dakota's largest park. According to Wikipedia, it also contains a spectacular herd of 1,500 roaming bison, and it includes a museum with exhibits on wildlife and South Dakota's history of mining prospectors. But best of all, there's numerous camp sites located throughout the Custer State Park. The best way to save money on a South Dakota vacation is to save the money that you'd spend on hotels, and spend the night in a beautiful campground instead.
The park's official site promises there's a wide variety of camp sites to choose from. ("Set up camp along a flowing stream, in the midst of pine forest, or near a mountain lake...") And if you're looking for more campgrounds across the rest of South Dakota, there's a handy map provided by KOA. Of course, there's other beautiful parks in South Dakota, including Badlands National Park (and the Buffalo Gap National Grassland). And besides beautiful scenery, there's also lots of locations for hunting and fishing, so if you're looking for an unforgettable outdoor vacation, South Dakota offers just about everything.
There's also an intriguing project to create an enormous monument to the Indian chief Crazy Horse. It's located about three hours from Mount Rushmore, and the work has been underway since 1948. It's an interesting counterpoint to the Mount Rushmore memorial, and is located in the town of Crazy Horse, on a street called "The Avenue of the Chiefs." While the monument isn't finished, there's educational material available about the project, and its deep significance for the Native Americans who work on it.
Two of the first Americans to come to South Dakota were Lewis and Clark, and you can visit many history sites marking their journey across the state. There's even a Lewis and Clark visitor center (built by "Lewis and Clark Lake") where you can learn more about their historic exploration of the newly-acquired Louisiana Purchase back in the early 1800s. But because much of South Dakota is still wilderness area, there's many parts of the state which still look just as beautiful!