From WoWWiki

The Black Vault is located inside Blackrock Depths, within Shadowforge City. It is accessed through a door situated between the Domicile and the Hall of Crafting. It is initially guarded by Warder Stilgiss and the darkhound Verek. Opening all the twelve coffers inside with Relic Coffer Keys will summon Watchman Doomgrip and four golems, which have to be defeated in order to receive the Heart of the Mountain.

Subzones of Blackrock Depths (Blackrock Depths regions)
The Black Vault • Chamber of Enchantment • Dark Iron Highway • Detention Block • The Domicile • East Garrison • The Grim Guzzler • Hall of Crafting • Halls of the Law • The Imperial Seat • The Iron Hall • The Lyceum • The Manufactory • The Molten Bridge • Mold Foundry • Ring of the Law • Shadowforge City • Shrine of Thaurissan • Summoners' Tomb • West Garrison