"If you're looking for a bright center of the Universe, you are on the planet it's farthest from."
----- Luke Skywalker to C3PO, Star Wars, Episode IV
With either theory, BB or Steady State there would not be a "center" at all.
-----BBT claims spacial expansion in all directions, therefore no center exists
-----SST claims the universe is unbounded and infinite, therefore no center exists
As for galaxies moving, our Milky Way as part of the local group and Virgo super cluster are being pulled at about 600 to 1000 miles per second toward THE GREAT ATTRACTOR
, a huge and mysterious gravity well located somewhere in the direction of Centaurus. Of course, our planet and solar system are going along for the ride.
For an interesting article on galactic motion and our relative position, check out this link----
Welcome to Altair4 gentlemen. We have two moons, a beautiful green sky, and we are only 16 light years away. Come visit anytime.