Talos II was the second planet in the Talosian planetary system. The planet had no moons. This system was located in the Talos star group, which was a region of space in the Alpha Quadrant. This planet was located at 1.8 astronomical units from the binary stars Talos A and Talos B. (TOS: "The Cage", "The Menagerie, Part I"; Star Trek VI: The Undiscovered Country, production art)
Background
The planet was never mentioned in dialog; this name came from a map of the Talosian system.
"The Explored Galaxy"
The location of Talos on "The Explored Galaxy" wall chart
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Talos was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in this quadrant. This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".
Star Trek: Star Charts
Talos II was classified as a H-class planet. In 2378, Talos II was located in or near Federation space, in the Alpha Quadrant. (pgs. 40-41, "United Federation of Planets III")