(covers information from several alternate timelines)
"Location: Delta Vega. Class M planet, unsafe."
Delta Vega was an icy class M planet in the Vulcan system, in the Alpha Quadrant. Its orbit carried it near enough to Vulcan that the other planet could be seen from Delta Vega's surface. There were at least two native, predatory species present on the planet: the drakoulias and the hengrauggi.
Ambassador Spock, after arriving to the past from 2387, was captured by Nero and marooned on the planet, so that he could witness the destruction of Vulcan at Nero's hands. Coincidentally, a young James T. Kirk was later marooned on Delta Vega by Commander Spock, and the two subsequently met Scott and Keenser there. (Star Trek)
This planet's location in the Vulcan system is assumed based on its proximity to Vulcan, close enough for Spock to witness its destruction with the naked eye as seen in the mind meld sequence. According to writer Roberto Orci, this was meant to be "impressionistic for a general audience". He thought of Delta Vega as being in an orbit close to Vulcan's, and that the original idea – having Spock view the planet's destruction through a telescope or some other device – "[wasn't] very cinematic". 
The Star Trek: The Original Series first season episode "Where No Man Has Gone Before" was set, in part, on a planet named Delta Vega, located near the galactic barrier. Although the planet in Star Trek was located in the Vulcan system instead, Orci and fellow writer Alex Kurtzman named it after the classic one. Orci has said: "We moved the planet to suit our purposes. The familiarity of the name seemed more important as an Easter egg than a new name [would have been]." 
In the film, Delta Vega was to have been a desert planet like its television counterpart, and Kirk was to find Spock and Scotty in a Mos Eisley-style environment. Yet script revisions made it an ice planet, and the aliens which might have populated its bazaar were dotted around the film instead, as mentioned in various Barney Burman interviews. (Star Trek - The Art of the Film)
Since the film production originally considered shooting some scenes in Iceland, it is thought that any such scenes would have represented Delta Vega.
According to the comic book adaptation of the movie, on page 103, the Starfleet outpost was designated Hunter.
The adaptation of "Where No Man Has Gone Before" in the first and second issues of IDW Publishing's Star Trek: Ongoing comics series proceeded from the notion that the Delta Vega near Vulcan was an entirely different planet from the Delta Vega featured in the original series. However, the comic also depicted both planets as being in the alternate reality.