Thanks to Marcus Lindroos
There are computer panels throughout the base, but the main data centre facilities seem to be in Main Mission/Command Centre, and in one or more Computer Rooms.
The side wall of Main Mission is composed of 32 feet (9.75m) of computer panels. Each computer wall section consists of 2 x 8 individual computer panels. According to Guardian Of Piri, the top-level functions of the computer are located here.
In Year Two, Command Centre has a new set of panels with a different design. These panels are only seen in Command Centre (the X5 Computers are seen elsewhere). The panels were originally used in the "Into Infinity" film, and thus bear captions such as "Yaw", "Pitch", "Roll", "Trim". In Brian The Brain it is identified as a "mark ten holographic programming" and we are told it does not speak. Presumably this is a separate computer to the Central (X5) Computer, but sharing the same network. The Command Centre computer may be specifically designed for spacecraft operations (hence the navigation panels) and astronomy, which would be monitored from this room (Main Mission was designed primarily for monitoring internal systems, and would have been less suitable after the Moon left Earth orbit).
The "Computer Room" is seen in Black Sun and (slightly different) in Space Brain; a "Computer Service Area" is seen in The Seance Spectre.
If the Computer is deactivated, it will only run in "auxiliary services" mode providing essential life support and communications control functions. As seen in Guardian Of Piri, Space Brain and Black Sun the deactivation can be requested using the commander's commlock or from a dedicated computer panel (labelled "Auxiliary services only" button in Main Mission, "Essential services only" in the Computer Room, but an identical button. ) More details
Copyright Martin Willey
Thanks to Marcus Lindroos