User blog comment:Arbington/The Next Cycle/@comment-2094653-20120803225240/@comment-1221773-20120804180547

In response to an earlier point of yours, Reaper central isn't right next to batarian space. When Sovereign was defeated in 2183, the Reapers woke up and started traveling to the galaxy. That trip took three years (give or take a few months. Destroying the Alpha Relay caused a six month delay for the Reapers), and the Reapers can travel 30 light-years in a 24-hour period, which is over twice the speed of any starship produced by the modern galaxy.

Now, assuming the Reapers' rate of travel is consistent during their trip, they traveled an approximate distance of 32,000 light-years. Note that this is about a third of the diameter of the Milky Way galaxy. So, Reaper central is located ~32,000 light-years away from the edge of the galaxy and batarian space. Even if the galaxy's races could find Reaper central in the midst of all that nothingness, it would still take them six years to travel there with current tech and six years to return, unless they could use the Citadel relay.