Tower

The Black Star Headquarters is the central base for the Black Star army, and is an important setting first introduced in Chapter 3 of the Black★Rock Shooter ~Innocent Soul~ manga.

The base takes responsibility of purifying souls gathered by soldiers of the Black Star army.

Vault of Souls
It is the room where souls that could not be purified are trapped in. The souls in this place are very strong and hostile, which may be because they are unpurified.

Gateway to Heaven
According to Dead, after souls are completely purified they are raised in a cage to the portal to Heaven. The history, characteristics, or what happens after entering are currently unknown.

Rooms
Apparently each Black Star has their own room with their familiar. They live here when they do not have a mission.

Black Star Stock
It's a warehouse full of cages containing the newly formed Black Stars. When a familiar needs a new partner they look for one in this place.

Information Room
On the floor there are a podium with information about the new mission of each Black Star, such as the sector it is in, information about the soul's illusion and its strength. Apparently, Hazama is classified in various sectors controlled by the organization. The different classes souls are classified with letters from D to A.

Board of Governors
It is not known if this room is actually inside the building but it is the meeting site where the six leaders of Hazama (Ouru, Ram, and 4 other mysterious figures) discuss the affairs of Hazama. A game board with white and black discs is seen here, which may have the ability to spy on Black Stars, as Ram was spying on Rock with the board.

Trivia

 * The game board that was seen in the Board of Governors resembles the Chinese board game Go.