Final Exam - S1-E1
Continuity mistake: After the Titans are evicted from their home and grieve over their loss, before Robin re-enters, as the Titans are gazing at the ocean, Cyborg's arms are attached to him, despite having lost his right one, which is still in Gizmo's possession.
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll