Vault 21

 is one of the Vault-Tec Vaults, located in or near Las Vegas, Nevada. Its purpose in the Vault Experiment is unknown. Mitchell likely comes from there.

Appearances
A Vault 21 jumpsuit appears in Fallout: New Vegas, so it's very likely that so does the vault itself. Doctor Mitchell that heals you in the beginning gives his old vault suit to you instead of your old ruined clothes he also gives you his old Pip-Boy 3000 (reference: Xbox Magazine, April 2010).