(covers information from several alternate timelines)
Babel was the code name for a planetoid in neutral space used by United Earth and later the United Federation of Planets as a venue for conferences. Relative to Tellar Prime, it was located on the opposite side of Andorian space. (ENT: "Babel One") Babel was located in the Alpha Quadrant and its location in the Milky Way Galaxy was depicted on a Federation star chart in 2293. (Star Trek VI: The Undiscovered Country, production art)
The planetoid 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.