I'll try to rephrase Cmac22's question (and he should correct me if I did wrong here).
At which place in the universe did the big bang take place?
After the big bang, everything started to expand, in every direction.
It's like a firecracker... the firecracker is the center of its own explosion, but after it exploded the little pieces are all over the place, but they are distributed in a circle (or sphere) around the place where the firecracker originally was.
I personally believe that there was space at the moment of the big bang. An infinite space around some sort of mega-supermassive black hole. The big bang was nothing but a black hole which spit out all its matter.
According to my view, there is a center, namely where the supermegamassive heavy black hole was when it blew up. (Sorry for inventing my own words here).
Undoubtedly others have a more complex view. I'm a chemical engineer, and I think of the world and universe as a thing you can touch, and as a place which works according to our earthly laws of physics (those laws you can see with your own eyes and feel with your hands).