From the Wiki (and I believe the guide says the same thing)
"This was Vault-Tec's base of operations around the DC area."
There was likely at least one HQ in every state, possibly in every city.
From the http://fallout.wikia.com/wiki/Fallout_Bible_1 (under "Vault System":
Basically, the Vaults were never intended to save the population of the United States. With a population of almost 400 million by 2077, the U.S. would need nearly 400,000 Vaults the size of Vault 13, and Vault-Tec was commissioned to build only 122 such Vaults. The real reason for these Vaults was to study pre-selected segments of the population to see how they react to the stresses of isolationism and how successfully they re-colonize after the Vault opens. Some of the experiments include:
Vault 8 - A control Vault, intended to open and re-colonize the surface after 10 years. Vault City is the result. Unfortunately.
Vault 12 - In order the study the effects of radiation on the selected population, the Vault Door was designed not to close. This is the Necropolis Vault... and the ghouls were the result.
Vault 13 - Intended to stay closed for 200 years as a study of prolonged isolation, the broken water chip forced the Overseer to improvise and use the Vault Dweller as a pawn. Later study of the Vault 13 records by the Enclave led them to their current plan to end the war.
Vault 15 - Intended to stay closed for 50 years and include people of radically diverse ideologies. Gathered from what you hear from Aradesh in Fallout 1, he has quite a bit of multi-cultural flavoring to his speech.
Vault 27 - This Vault would be overcrowded deliberately. 2000 people would be assigned to enter, double the total sustainable amount. The location of this Vault is unknown.
Vault 29 - No one in this Vault was over the age of 15 when they entered. Parents were redirected to other Vaults on purpose. Harold is believed to have come from this Vault.
Vault 34 - The armory was overstocked with weapons and ammo and not provided with a lock.
Vault 36 - The food extruders were designed to produce only a thin, watery gruel.
Vault 42 - No light bulbs of more than 40 watts were provided.
Vault 53 - Most of the equipment was designed to break down every few months. While repairable, the breakdowns were intended to stress the inhabitants unduly.
Vault 55 - All entertainment tapes were removed.
Vault 56 - All entertainment tapes were removed except those of one particularly bad comic actor. Sociologists predicted failure before Vault 55.
Vault 68 - Of the one thousand people who entered, there was only one woman.
Vault 69 - Of the one thousand people who entered, there was only one man.
Vault 70 - All jumpsuit extruders fail after 6 months.
Vault 106 - Psychoactive drugs were released into the air filtration system 10 days after the Door was sealed.
Rumor has it there were 122 different vault experiments. For Fan Fiction purposes, a lot of these vault experiments have been left open for you to play around with
Communication between experiments would have contaminated the experiments; but what if? The major concern is that the vault dwellers not learn that they are being experimented on, allowing contact between vaults increases the risk that the experiment will be detected.
So, the vaults were social experiments (according to a developer) and weren't ment to save humanity, Why?
The vault-tec company, or whoever contracted them, did not believe that humanity would be wiped out by a nuclear war (and by FO lore, it wouldn't have been), and that the US was just going to keep running as usual. So there may not have been a vault for the vault-tec officials. But why not have one, after skimming funds from 122 vaults they could have surely build an extra one on the sly.
Vault 0 is the governments vault, and may have been able to monitor the other vaults.
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Note that it says that "there were 122 different vault experiments," different experiments, not vaults, and this number may not include control vaults; so you can have a vault 300, and may have vaults with higher numbers. Vaults near strategic sites (or that had a lot of pull in the government) would have been built first. If you assume that state capitals have an average of five vaults you have a minimum of 250. Adding in other major cities (and the annexing of Canada) you can easily exceed 300 vaults.