The computer center, also known as the computer room, was a section of a facility or a starship that was responsible for the coordination of all information storage and transmission activity.
Federation computer centers[]
Humbolt in the computer center of Starbase 11
In 2267, Commander Spock sneaked into the computer center of Starbase 11 in order to forge a voice transmission to the USS Enterprise as part of a plot to commandeer the ship. Spock was caught by Chief Humbolt, a technician assigned to the computer center, who attempted to stop him, but Spock incapacitated him with a Vulcan nerve pinch. (TOS: "The Menagerie, Part I")
Sometime in the 2270s, Leonard McCoy didn't care for the sickbay of the refit Enterprise, saying it was "like working in a damned computer center." (Star Trek: The Motion Picture)
In the final draft script of "The Menagerie", Starbase 11's computer center was described as "a complex communications and library-computer center, the automated heart of the Star Base."
The computer center as seen in "The Menagerie" was a re-dress of the Enterprise engineering set.
In 2384, the location of the computer room on the USS Dauntless was labeled in a master situation display. This room was located on Deck B. This room was listed with other rooms, technologies, and systems for engineering in an operations panel on the main bridge. Furthermore, this room was listed with other areas of the ship on a bridge conn panel. (PRO: "Mindwalk")