I think you're mixing up terms. Homogeneity means the same everywhere. So it is directly contrary to the notion of us being the center.
You probably mean isotropy, which means the same in every direction. If the universe is isotropic but not homogeneous as viewed by us, then this means moving some distance away it would cease to look isotropic. Exactly how far we'd have to move, then, depends upon how things change as we move away from the Earth. But at the very least we'd have to move far beyond our own galaxy, which is around 100,000 light years across (As in close to a billion billion miles). We'd be talking millions of light years at least, perhaps hundreds of millions of light years, in order to see any difference.