Starbase 185 was a Federation starbase facility which was in operation in the late 24th century, and was located around 7,000 light years from System J-25. (TNG episode: "Q Who?") In the late 2370s, the starbase was under the command of Admiral de la Fuego. (TTN novel: Taking Wing)
In late 2379, the USS Titan was due to stop off at the base after departing from the Utopia Planitia Fleet Yards. Unfortunately, the medical relief mission to Romulus delayed the starship arrival.
Doctor Xin Ra-Havreii was hoping to be able to secure a fresh supply of real levithi nuts on the base, but the delay meant that he had to acquire another supply. (TTN novel: Taking Wing)
Captain Jean-Luc Picard contacted the starbase to inform Starfleet Command of Q's appearance. (TNG novel: Q & A)