From WoWWiki

The Vault of Ironforge is located in the Commons in the dwarven city of Ironforge, across from the auction house. This bank is one of the many that can be accessed by players. Entering this area can be extremely chaotic, since it is known for extreme and sudden lag spikes due to being the busiest part of the busiest city on the Alliance side.

Subzones of Ironforge
The Commons • The Gates of Ironforge • The Great Forge • The Forlorn Cavern • Hall of Arms • Hall of Explorers • Hall of Mysteries • Hall of Thanes • The High Seat • The Library • The Military Ward • The Mystic Ward • Tinker Town • Vault of Ironforge