Badlands and Black Hills
The Badlands and Black Hills are part of South Dakota.
From the sky, you will likely have only one viable option for a point of entry: Rapid City Regional Airport IATA: RAP. Flights arrive regularly from Denver, Chicago, Salt Lake City, and Minneapolis, as well as a twice weekly nonstop from Las Vegas.
Without a car, you won't go far. I-90 is the sole interstate in the region, running east-west, skirting Black Hills NF and Badlands NP to the north, and passing through Rapid City. It goes on to Sioux City in the east, and west to Wyoming to connect with I-25, which leads south to Denver.
The main sights are indisputably the cyclopean sculptures at Mount Rushmore National Memorial and the embryonic Crazy Horse Memorial, both of which are right by Custer. Wind and Jewel Caves, as well as Badlands National Park are also well worth a visit. But if you are here to just snap photos of a few main attractions, you are going to miss the point. This is beautiful, big, wild country, and to appreciate it, you'll need to spend days driving or hiking around to take in the glorious scenery, gawk at wildlife, wonder at the night stars, and enjoy the fresh, clean air.