Starbase 117 was a Federation starbase administered by Starfleet.

The Ferengi Par Lenor and Qol were sent via shuttle to Starbase 117 by the USS Enterprise-D following their part in an accident that befell Kriosian Ambassador Briam while attempting to purchase Kamala in 2368. (TNG: "The Perfect Mate")

This starbase was only mentioned in dialogue.
According to Star Trek: Star Charts (p. 63) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Starbase 117 was located in the Beta Quadrant.