Later in the same year, a shuttlecraft was stolen from the starbase by Lokai, a fugitive from the planet Cheron, two weeks before it was found by the Enterprise. (TOS: "Let That Be Your Last Battlefield")
Presumably, Starbase 4 was located in the Alpha Quadrant.
Starbase 4 appeared in the Pocket Books novel Memory Prime, written by Garfield Reeves-Stevens and Judith Reeves-Stevens. The base was under the command of Commodore Montana Wolfe, and had its insignia in the rough shape of the Orion constellation.