In 1900 two prospectors, Frank and Albert Michaud, felt cold air blowing out of a hole in a canyon wall west of Custer. The hole was too small to climb through, so they widened it with dynamite and found the walls beyond lined with calcite crystals. They called it Jewel Cave, built walkways, and tried to make a business of it. The business never really worked. The protection did: in 1908 Jewel Cave became a national monument, the first anywhere established specifically to protect a cave.
What nobody understood in 1908 was the scale of what they had. Survey has now mapped over 220 miles of passage, making Jewel Cave the fifth longest cave in the world and the second longest in the United States, and exploration has not finished. Airflow measurements at the entrance suggest that the mapped portion is a fraction of the whole, because the volume of air moving in and out implies far more space behind it than has been walked.
That airflow is the cave's other claim. Jewel Cave is one of the best documented breathing caves known, its passages drawing air in and pushing it back out as the barometric pressure outside rises and falls. The Michauds found it precisely because it was exhaling on a cold day.
The cave sits in the Black Hills of South Dakota, about 13 miles west of Custer and 13 miles from Wind Cave, which is also a breathing cave and also enormous. Despite the proximity no connection has been found between them.
Tours are guided and vary sharply in difficulty, from the Scenic Tour on a paved and lit route with several hundred stairs to a Wild Caving Tour that requires crawling through a concrete block sized opening to prove you will fit.
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Other places on the map within a couple of hours.