Altair VI was the inhabited sixth planet of the Altair system. The system was located in Sector 9, which was a region of space in the Alpha Quadrant.
Despite a long interplanetary conflict in this system in the years before, Altair VI was well known for its excellent shore leave facilities in 2267. In the same year a new president was to be inaugurated on the planet, an event of significant importance towards stability in the Altair system. The inauguration was expected to send shock waves as far as the Klingon Empire and therefore was attended by three Starfleet starships, including the USS Enterprise. (TOS: "Amok Time"; Star Trek VI: The Undiscovered Country, production art)
In 2285, Altair VI was a part of the Kobayashi Maru simulation at Starfleet Academy; the Kobayashi Maru claimed to be nineteen periods out of Altair VI. (Star Trek II: The Wrath of Khan)
The location of Altair VI on "The Explored Galaxy" wall chart
The location of Altair III on the tactical situation monitor
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. The Altair system, represented by Altair VI, was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in the Alpha Quadrant.This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game", and DS9: "In the Hands of the Prophets", "Cardassians".
According to the StarTrek.com
web site, Altair VI was the "center of the Altair system." 
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