(covers information from several alternate timelines)
Babel was an inhabited neutral planet of the Alpha Quadrant. This planet was used by United Earth, and later the United Federation of Planets, as a venue for conferences, which were mediated in council chambers. (TOS: "Journey to Babel"; TAS: "The Counter-Clock Incident"; ENT: "Babel One")
In 2293, the location of Babel in the Milky Way Galaxy was labeled in a star chart that was in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In 2366, in an alternate timeline, during the Federation-Klingon War, the location of Babel was labeled on a tactical situation monitor in the ready room aboard the USS Enterprise-D (TNG: "Yesterday's Enterprise", okudagram)
The planet was planned to host negotiations to settle trade disputes between the Andorians and the Tellarites and mediated by Starfleet on behalf of United Earth in 2154. However, the meeting was postponed due to tensions between the two powers caused by a raiding Romulan scout vessel in the area. (ENT: "Babel One")
In 2268, the Babel Conference was held there to determine Coridan's admission to the Federation. As such it was also the namesake of the Babel Resolutions. (TOS: "Journey to Babel"; TAS: "The Pirates of Orion")
In 2270, the USS Enterprise transported Commodore Robert April and his wife Sarah to Babel, where ambassadors from all Federation worlds had converged to honor April as he had reached his mandatory retirement age. (TAS: "The Counter-Clock Incident")
According to Star Trek Maps (page 24 & chart D), Babel was located in the Wolf 424 system. The Babel planetoid had three small moons called Zion, Ba and Ruim. Babel had a diameter of 4,200 km and orbited a red dwarf star.