Granite Mountain Records Vault
It was finished in 1965, and has been operational since 1966. More than underground its inside a massive granite rock. It even has its own natural water source, and the doors were designed to withstand a nuclear explosion at the base of Little Cottonwood Canyon.
http://www.lds.org/newsroom/showpackage/0,15367,3899-1--35-3-163,00.html
This article has a lot of details about it, but it is not without bias.
Steve G.