Stop 1: Wind Cave National Park
National Park offers several guided tours to the cave at affordable prices ($12). Timing is very convenient and it was very easy to purchase tickets at the visitor center. We arrived at 11am and were in the cave at 11:30 :) I can't say that this is one of the most beautiful caves I've ever seen, but it is very big and people are still surveying it. We spent ~ an hour in the cave.
Stop 2: Badlands National Park
Badlands surprised us in a very nice way: the territory of these unique pinnacles formations and prairies is massive! There are several view points along the scenic road and many different hiking trails which will lead you among the prairies or will give you an opportunity to walk on their tops.