How far are we from the edge of the Universe?
In the standard models of the Big Bang, there is no such thing as the "edge of the expansion front". The universe, as far as we can see and as far as standard cosmology assumes, is homogeneous and isotropic on the large scale, so there is no edge or anything analogous to an the shock front of an explosion.

According to the seven-year WMAP results [pdf], the proper distance to the surface of last scattering that emitted the cosmic microwave backgrounds is approximately $46.0\,\mathrm{Gly}$, which is basically as far as we can actually see. The true cosmological horizon slightly more distant that this, closer to $46.6\,\mathrm{Gly}$. What's beyond the horizon is not known.

Another cosmologically significant distance scale is the Hubble radius, at which the galaxies comoving with the Hubble flow recede from us at the speed of light. It is $c/H_0 = 13.9\pm0.3\,\mathrm{Gly}$.