This is core point of relativity. There is no absolute coordinate system whatsoever. Everything is defined as in relation to something else.
You're already there. Since all of space expanded from one point, by definition the Big Bang actually happened right here (and also over there) [1].
[1] http://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem
The best analogy I've seen is that of ants on a balloon. They live in what appears to them to be a two dimensional universe. As you inflate the balloon, they observe their own universe getting bigger. But the "point where the Big Bang happened" to them is not a point that even exists in their universe any more. They cannot get back there, since the higher third dimension does not exist in their universe.
It's better to think of the Big Bang as an unimaginably intense period of expansion and cooling of whatever substance the earliest universe was made out of (see Inflation theory). It was not an explosion that happened in a pre-existing spacetime.