There is no center to the source of the background radiation, as it is was created at a moment the universe was still a fairly homogeneous soup (apparently) with these photons being created (and absorbed) everywhere roughly in equal quantity.

Only after the universe became transparent did these photons become free, and since they were produced roughly homogenously in that soup there are everywhere in the same quanitity: a background radiation.

Since they were not produced in a localized event, they won't have a center. But since they're everywhere, they are a sort of absolute reference for how fast you're going (actually that's a new and interesting idea for me too, pretty neat).