Something as a those unknown vaults has my mind turning.... And created one in mind:
This pre-war vault had multiple gyms, basketball courts, and even a full-sized base diamond, however lacked the computer database, or even a security equipment. In an attempt to stave off morale loss and to cheer people up, this vault was designed to hold numerous famous sports player, along with commoners, in an attempt to keep people healthy, happy, and most importantly unaware. This vault was rather large in size, housing more than the standard thousand people, but more up to three thousand.
This vault was built with money from various national agencies attempting to secure their own protection in the wars, from Nike, Watson, ESPN, and numerous other sports companies.
True Purpose: Military Steroids
Like with most other vaults, this vault was also included in the Vault-tec master experiments, this one being subject to brand in innovated steroids. Like Vault 87's hypnotic suggestions to make super-soldiers, this vaults water system was laced with a liquid muscle growth and celluar regeneration chemicals, in attempts to see if they could achieve better results than the risky FEV at the time.
Sadly, over several years, the residents of Vault 41 broke down into two groups, those that survived and adapted to the treated water, left the vault. They now resides in what was once the Boston Metropolitan Area, while others moved north. Depending on which group you talked to, they refer to themselves as the Red Sockers, tribals who are excellent fist-fighters and throwers, able to throw a leather-incased stone far, or to hit something yards away, or as the NYanke's, tribals with outstanding armed skills, especially with basebats or pool sticks, able to sprint with lightining speeds, in short bursts.
Those who didn't adapt degenerate in mutanted men and women, grossly husky and muscular, now roaming the abandoned remains of Vault 41, bashing enemies to death.