Vega was an inhabited planetary system in the Alpha Quadrant. One of its planets was Vega IX.
The location of Vega was depicted on a star chart in astrometrics on the USS Voyager in 2376. (VOY: "Child's Play"; TOS: "Mirror, Mirror")
In 2399, a Federation star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters located Vega in the Alpha Quadrant. This system was in or near to Federation space. (PIC: "Maps and Legends")
In 3190, the location of Vega was labeled on a star chart used by Commander Paul Stamets for tracking the movement of the Dark Matter Anomaly through the galaxy. (DIS: "The Examples")
Vega is a real star system about 25 light years from Earth. The Vega colony, presumably at Vega, was established prior to 2151.
According to Star Trek: Star Charts (pp. 36, 44, 57; "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the primary of the Vega (Alpha Lyrae) system was an A-class star. In the 19th century, it was the capital system of the Vegan Tyranny (β). In the mid-22nd century, this system was an important trading 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.
There exists a picture of Steven Lance, who played a Rhaandarite, identifying him as a being from the planet Vega. This may be linked to early mentions of Vegans in the crowd. 
In the 1977 children's storybook The Prisoner of Vega, Klingons capture Queen Vanadala of Vega III and take over her planet.
In the game Star Trek Online, the Vega system was the site of a renewed Borg attack in 2409, and where the tutorial for Federation players takes place.