Starbase 214 was a Federation starbase administered by Starfleet.

Immediately after his arrest on the USS Enterprise-D in 2368, Berlinghoff Rasmussen was dropped off at Starbase 214. (TNG: "A Matter of Time")

This starbase was only mentioned in dialogue.
According to Star Trek: Star Charts ("United Federation of Planets III") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Starbase 214 was located in the Alpha Quadrant.