Delta Vega is a moon (or possibly a small planet) in the Vulcan System, at least according to this webchat with the film's writer, Bob Orci
How can Spock observe the destruction of his homeworld from the surface of Delta Vega. Even if Delta Vega wasn’t near the edge of the galaxy, you couldn’t watch the implosion from a neighbouring planet. You couldn’t see Earth from Mars either. Is Delta Vega a Vulcan moon or what?
Bob Orci: I prefer to think of Delta Vega as being in close orbit (although it could be a moon), but nonetheless, we like to think of that sequence as impressionistic for a general audience. In other words, Nero could’ve beamed Spock prime down to Delta Vega with a telescope or some other type of measuring device to allow Spock to experience the pain of perceiving the destruction of his home world, but that simply isn’t very cinematic.
Its similarity in name to the Delta Vega seen in the Original Series is a mere coincidence:
For the Trek fans, this film includes many little references. For
example you have Kirk dropped off on the planet Delta Vega, which was
seen in second Star Trek pilot. It is a cool reference, but didn’t you
also fudge canon by ignoring that Delta Vega was way out next to the
Orci: True. Yeah we did. We moved the planet to suit our purposes. The
familiarity of the name seemed more important as an Easter egg, than a
new name with no importance.