In 2267, the USS Enterprise traveled to this base following its mission to Deneva. Later that year, Commodore Stocker was assigned to command of the base and was transported there by the Enterprise. (TOS: "Operation -- Annihilate!", "The Deadly Years")
Presumably, Starbase 10 was located in the Alpha Quadrant.
This base was also mentioned in gaming reference books (The Triangle Campaign, Starfleet Operations Manual), novels (Pocket TNG: Red Sector), and comics (Gold Key TOS: "Sceptre of the Sun" and Peter Pan Records: "The Robot Masters").