Originally Posted by Aqua
While 8kly is canon, I doubt that Earth is near the center. They encountered the Klingons and Romulans etc. early on which would have confined their boundaries in those areas, Earth is probably within a couple hundred ly of the Federation's boundary.
Earth is meant to be located right along the border between the Alpha and Beta quadrants, I'd guess it wouldn't be too far from here to either the Klingon or Romulan Empires.