We present Galactic mean metallicity maps derived from the first year of the SDSS-III APOGEE experiment. Mean abundances in different zones of projected Galactocentric radius (0 < R < 15 kpc) at a range of heights above the plane (0 < |z| < 3 kpc), are derived from a sample of nearly 20,000 giant stars with unprecedented coverage, including stars in the Galactic mid-plane at large distances. We also split the sample into subsamples of stars with low- and high-[α/M] abundance ratios. We assess possible biases in deriving the mean abundances, and find that they are likely to be small except in the inner regions of the Galaxy. A negative radial metallicity gradient exists over much of the Galaxy; however, the gradient appears to flatten for R < 6 kpc, in particular near the Galactic mid-plane and for low-[α/M] stars. At R > 6 kpc, the gradient flattens as one moves off the plane, and is flatter at all heights for high-[α/M] stars than for low-[α/M] stars. Alternatively, these gradients can be described as vertical gradients that flatten at larger Galactocentric radius; these vertical gradients are similar for both low- and high-[α/M] populations. Stars with higher [α/M] appear to have a flatter radial gradient than stars with lower [α/M]. This could suggest that the metallicity gradient has grown steeper with time or, alternatively, that gradients are washed out over time by migration of stars.