Special Relativity is as special as Special Olympics. It's considered special, yet it says no frame of reference is special. Double standards much? [/humor]
Anyway. The center of the Universe (note - Universe, not Space) is indeed only a factor if the universe is finite. Furthermore, if the universe is uniformly chaotic, then its center would be no better than any other point of the universe, even if it's finite.
But you have to factor something in. Let's presume for a moment that by some staggering violation of laws of probability, the center of the universe-creating explosion (calling it a "bang" is equally diminuitive, if you ask me) left a tiny empty space right in the universe's center of mass, large enough to put a ship in. All forces cancelling out, you would be at zero velocity and zero acceleration, motion of the entire universe would only be the motion of the universe, not your motion as part of the universe.
While not special by any stretch of the principles of special relativity or ambient energy, you'd still be in a universe's dead zone. Your position and speed would not have universe as a factor, unlike Neruz'z left foot, which inherits its motion from the Earth it stands on, which inherits its motion from the Sun it orbits, which inherits its motion from the Galaxy it is part of, which kinda shuffles forward due to anything the Universe did that scared it so much.
You could say in other words, that the point I'm speaking of is the average position of all matter and energy in the universe. Or the universe's center of mass. Presuming the Big Bang as the universe's origin, the average velocity of all matter and energy in the universe relative to that point would be close to zero.
But anyway, that point is purely theoretical. And yes, not really special unless you count those interesting qualities.
And finally, why does everyone use the words Universe and Space like they're interchangeable? What, the concept that the Universe exists within the Space is that impossible? It would even explain acceleration of the universe's expansion.