(covers information from several alternate timelines)
The Vega colony was an Earth colony on a planet orbiting the star Vega. This colony was located less than ninety light years from Sol. It was one of the earliest Earth colonies established, along with Alpha Centauri and Terra Nova. Established as an outpost, Vega colony was, for many decades, located on the frontier of known space. By the time it became an important trading partner of Earth and other worlds, it was referred to as a colony. In the 2250s, Vega colony was several weeks away from Rigel VII at the maximum speed of a Constitution-class heavy cruiser. (TOS: "The Cage", "The Menagerie, Part I", "The Menagerie, Part II"; ENT: "Terra Nova", "Fortunate Son", "Two Days and Two Nights", "Twilight")
In 2152, Admiral Forrest speculated that an escape pod-like vessel, found by Enterprise NX-01, might have been launched by Vega colony. However, the small vessel was later discovered to be a timeship from the 31st century. (ENT: "Future Tense")
In an alternate timeline, created by Jonathan Archer being infected by interspatial parasites, the Xindi destroyed Earth in 2154 and then proceeded to annihilate all other Human settlements, including Mars, Alpha Centauri, and Vega colony. (ENT: "Twilight")
In 2254, the USS Enterprise planned to make use of the medical facilities at the Vega colony to take care of the crew injured on Rigel VII and replace the personnel who needed hospitalization. (TOS: "The Cage", "The Menagerie, Part I")
In 2328, this was the destination for passengers traveling from Tycho IV Spaceport via commercial transport. David S. Grant, James Holt, and Scooter T. Rocketboy traveled on the SS Kogin, and Richard Sarstedt on the SS Wisconsin. (TNG-R: "Inheritance", okudagram)
The real-world star Vega (Alpha Lyrae) is located approximately 25 light years from Sol, which is in agreement with "Two Days and Two Nights", where it is stated that the NX-class Enterprise set a milestone by becoming the first Earth ship to travel 90 light years away from the Sol system.
According to Star Trek: Star Charts (p. 36 & 44; "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Vega (Alpha Lyrae) system was located in the Alpha Quadrant. In the mid-22nd century, this important trading system was a destination on the Earth trade routes, and it traded with Draylax and Sol. In 2254, the Enterprise traveled to the system after visiting the Talos star group. In the late 24th century, the system was a destination on a major space lane. In 2378, the Vega Colony, on Vega IX, was listed as a Federation member.
In Star Trek Online, the Vega colony was the site of the Borg reemergence in the galaxy during the year 2409, Starfleet attempted to evacuate Vega colony while engaging the Borg fleet in orbit. This location served as the tutorial for the game as the player attempted to defend the evacuees and then repel the invasion force.