Vault 21

 is one of the Vault-Tec Vaults, located in or near Las Vegas, Nevada. Its purpose in the Vault Experiment was gambling, and all conflicts in the Vault were solved through a toss of the dice. Mitchell comes from here.

Layout
The Vault has been converted into another casino, so it's likely that the Vault was built in or very close to Las Vegas.

Appearances
Vault 21 appears in Fallout: New Vegas.