The correct way to write the sentence is:
We went to Mount Rushmore, which is a large mountain with the faces of presidents found near Keystone, South Dakota.
This version correctly capitalizes "Mount" and "Rushmore" because they are part of a proper noun (the name of a specific location), and "Keystone" and "South Dakota" are also capitalized as they are proper nouns referring to a specific place. "Mountain" should be lowercase since it is a common noun in this context.