Cathedral Cave is located in Onondaga Cave State Park. You'll have a one-third mile walk up Deer Run Trail to the cave's entrance, after which the tour lasts about 90 minutes, covering 1.66 miles. The cave's temperature is 57ºF (13ºC). The tour is more strenuous than the Onondaga Cave tour and round trip. Check the website for tour times and fees.
Most, if not all, of Cathedral Cave is hollowed in the Gasconade dolomite, which was laid down approximately 440 million years ago. The cave consists of two distinct sections: a dimensionally larger and presumably older passage with its entrance high on the campground valley hillside; and the much longer, narrower, younger and lower (both in passage size and elevation) cave stream passage, which intersects the stream at right angles near the Cathedral column - the top speleothem in the cave.