Final answer:
The state with the Black Hills, Mount Rushmore, and other historic landmarks is South Dakota, known for its rich cultural and natural history.
Step-by-step explanation:
The state that has the Black Hills in the southwest, and includes notable landmarks such as Mount Rushmore, Wind Cave National Park, Jewel Cave National Monument, Custer State Park, the Crazy Horse Memorial, the city of Deadwood, Prairie Hills in the east, and the Badlands is South Dakota. It is a place of immense historical significance, particularly in terms of its relationship with the Native American tribes, such as the Lakota Sioux, who consider the Black Hills to be sacred. The area has been the site of numerous historical events including the Battle of the Little Bighorn and the creation of the Mount Rushmore National Memorial. Visitors can also explore the region's cultural history at sites like the Crazy Horse Memorial, which honors the Native American warrior, and Deadwood, a town famous for its gold rush history.