The End (2) - S4-E13
Trivia: While the Titans fight their own evil sides summoned by Trigon, the evil Cyborg taunts the good Cyborg about having no mother. As a matter of fact, in the mainstream comic series Cyborg's mother died because of a botched experiment by his father, which summoned an interdimensional monster. It was also on that day that Cyborg received his cybernetic prosthetics due to injuries the monster had inflicted on him.
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll