Going with the balloon idea, the universe is the surface of the balloon. A sphere doesn't have a center on the surface.

We could say that the center of the sphere is where the big bang started. The distance to the center of the expansion is 13.7 billion years. It doesn't have a distance in x,y,z coordinates, because those are all on the surface, and it's kind of futile to attempt to understand time as a fourth dimension in this regard. We don't know if the universe is spherical at all. It's just a description used to portray the expansion. The expansion is also happening faster than light, which makes it impossible to convert the age of the universe to a size. The universe is bigger 13.7 billion light years, perhaps even infinite. Infinity doesn't have a center either.