Deneb IV was located in the Alpha Quadrant. It was one of four notable planets in this system; the others were Deneb II, Deneb V, and Deneb XX. (TOS: "Where No Man Has Gone Before", "I, Mudd", "Wolf in the Fold", Star Trek VI: The Undiscovered Country, production art; TNG: "Encounter at Farpoint"; DS9: "Whispers")
Some time prior to 2265, a young James T. Kirk and Gary Mitchell came to this planet, where Mitchell got involved with a woman. Kirk later stated that he'd been worried about Mitchell ever since that night. As a pun Mitchell referred to the girl as a nova.
Also during the mid-23rd century, inhabitants of Deneb IV communicated telepathically. In at least three cases during the 2260s, Gary Mitchell carried on long telepathic conversations with select Deneb IV natives and scored eighty percent or higher on comprehension. (TOS: "Where No Man Has Gone Before")
By 2364, the Bandi had seemingly constructed Farpoint Station, a base which they subsequently offered to Starfleet. Intrigued by the extremely short time in which it was built, Starfleet sent the USS Enterprise-D on its maiden voyage to the planet in order to investigate the base. It was subsequently discovered that the station was in fact a spaceborne entity, enslaved by the Bandi. Upon this discovery, the entity was released, and Starfleet and the Bandi began planning to reconstruct the station. (TNG: "Encounter at Farpoint")
Behind the Scenes
Michael Okuda recalled how Deneb IV was originally depicted in "Encounter at Farpoint"; "The beautiful shot of Deneb IV was actually a matte painting done by Industrial Light & Magic, and that was done on film." Speaking shortly before the release of Star Trek: The Next Generation - The Next Level Blu-Ray sampler, Okuda also compared the remastered version of the planet with the original, saying, "The planet is pretty much dead on with what was done in the original shot."  He was referring to the planetary shot of Deneb IV in this interview.
The planet surface of Deneb IV, including Farpoint Station and Bandi city, was in actuality a maquette, built by maquette specialist Gregory Jein. It, combined with a background matte painting, was filmed at ILM by visual effects cameraman Robert Hill. (The Official Star Trek: The Next Generation Magazine, issue 2, January 1988, p. 41)
"The Explored Galaxy"
In "The Explored Galaxy" star chart, Deneb 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 the Alpha Quadrant. This chart was first seen, chronologically, in 2293. (Star Trek VI: The Undiscovered Country) The 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".
- Deneb Kaitos IV, also known as Beta 16 Ceti IV, was the planet Deneb IV mentioned in "Where No Man Has Gone Before".The planet had one moon. In the mid-22nd century, this planet was a destination on the Vulcan trade routes. (pgs. 41, 44, "United Federation of Planets I")
- Alpha Cygni IV was the planet Deneb IV seen in "Encounter at Farpoint". The planet was located 3,320 light years from the Sol system. As the homeworld of the humanoid Bandi, the planet was united under a single government, Bandi, which had its seat in Farpoint. In 2364, this world signed a treaty with Starfleet. Under the terms of this treaty, Starfleet would administer Farpoint Station. Between 2364 and 2378, this world was admitted to the Federation. In the census of 2370, there were counted an estimated 450 million Bandi living on the planet. Points of interest were Farpoint Station and Old City. (Pgs. 12-13, 34, 41, "United Federation of Planets I")