Multiple realities(covers information from several alternate timelines)
Starbase 23 was a Federation starbase administed by Starfleet. This base was located near the Romulan Neutral Zone. (TNG: "All Good Things...")
In 2269, it was the nearest starbase to Terra 10 and the Arachna supernova. (TAS: "The Terratin Incident")
In 2369, after the metaphasic shield incident, Dr. Beverly Crusher was to take a shuttle from the USS Enterprise-D to Starbase 23, where a transport ship would pick her up and bring to Earth for a board of inquiry at Starfleet Medical. (TNG: "Suspicions")
In 2370, Starbase 23 was the closest Federation outpost to the Devron system. (TNG: "All Good Things...")
In an alternate 2370 created by the the anti-time eruption, Captain Picard ordered Counselor Troi to contact Starbase 23 to see if the effects of the temporal anomaly in the Devron system had spread. (TNG: "All Good Things...")
In an okudagram in TNG: "Sins of the Father", this was originally the starbase that Kahlest had her injuries treated. The dialogue changed the designation of this starbase to 24.