(covers information from several alternate timelines)
Tau Ceti was the primary of the inhabited Tau Ceti planetary system. There were several planets in the system that were inhabited: Tau Ceti III, Tau Ceti IV, and Tau Ceti Prime. Tau Alpha C was also located in the system. (Star Trek II: The Wrath of Khan; TNG: "Conspiracy", "Remember Me", "Journey's End"; VOY: "Coda")
Tau Ceti was located in the Alpha Quadrant. Its location was depicted on two Federation star charts. In the first chart, showing the location of this star in the Milky Way Galaxy, was first seen in 2293. It was depicted as being near Sol, Alpha Centauri, and Sirius. (Star Trek VI: The Undiscovered Country, production art)
In 2364, on several occasions that year, viewscreen readouts aboard the USS Enterprise-D showed the location of Tau Ceti, in the form of charts from the Enterprise library computer. (TNG: "The Naked Now", "The Last Outpost", "Conspiracy") The system was also quite some distance away from Starbase 133, at warp 9.5 it took 123 days to get there. (TNG: "Remember Me", "Journey's End")
At some point prior to 2268, the USS Enterprise, under the command of Captain James T. Kirk, engaged and defeated a Romulan vessel near Tau Ceti, using the Cochrane deceleration maneuver. (TOS: "Whom Gods Destroy")
Tau Alpha C was the home of The Traveler and others of his kind, (TNG: "Where No One Has Gone Before") located in the Tau Ceti system (TNG: "Journey's End") Members of the Travelers species were capable of existing outside of time, and had very little interest in associating with other more primitive species, until the 2360s, when they became aware of Humans like Wesley Crusher. (TNG: "Where No One Has Gone Before")
In 2155, in the mirror universe, Tau Ceti was the system in which the Terran Empire lost twelve ships in a battle against alien rebels. Propaganda had spread that this was a major victory for the Terran Empire, when in fact it was a sign they were losing. (ENT: "In a Mirror, Darkly")
In 2367, in an alternate universe created by the thoughts of Doctor Beverly Crusher inside a warp bubble, Tau Alpha C disappeared along with the entire universe when the warp bubble began to collapse. (TNG: "Remember Me")
This chart naming stars within 20 light years of Sol was drawn by Rick Sternbach for the Star Trek Spaceflight Chronology in the late 1970s. Found on page 77, this chart showed Earth commercial and exploration routes after the use of warp drive began. Tau Ceti was the destination on an exploration route.
"The Explored Galaxy"
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Tau Ceti 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".
From the mid-22nd century, Tau Ceti was located in or near Federation space, in the Alpha Quadrant. The planet Kaferia was located in this system. It was the third planet from the sun. Tau Ceti was a G-class star with a magnitude of +5, which was the same brightness as Sol. (pg. 44)
According to the novel Enterprise: The First Adventure, Tau Ceti was located along the Romulan Neutral Zone and the inhabitants of Tau Ceti II were widely regarded as possessing great mineralogical expertise, using sapphires as the local currency.