We identify "red clump stars''-core helium-burning giants-among 2MASS stars and use them to measure the run of reddening with distance in the direction of each of the Galactic anomalous X-ray pulsars (AXPs). We combine this with extinction estimates from X-ray spectroscopy to infer distances and find that the locations of all AXPs are consistent with being in Galactic spiral arms. We also find that the 2-10 keV luminosities implied by our distances are remarkably similar for all AXPs, being all around similar to 1:3 x 10(35) ergs s(-1). Furthermore, using our distances to estimate effective blackbody-emitting radii, we find that the radii are tightly anticorrelated with pulsed fraction and somewhat less tightly anticorrelated with blackbody temperature. We find no obvious relationship of any property with the dipole magnetic field strength inferred from the spin-down rate.