Starbase 1 was a Federation starbase administered by Starfleet. It was located 100 AUs from Earth. In the 2250s the starbase was home to over 80,000 Federation personnel.
During the Federation-Klingon War, the starbase was conquered by the House of D'Ghor. The battle resulted in the deaths of many of the top leaders of Starfleet Command and at least three Starfleet ships destroyed. (DIS: "The War Without, The War Within")
The distance from Earth would seem to indicate that this outpost was located in the inner Oort cloud of the Sol system.