  The mid-infrared (MIR) spectra of dense photodissociation regions (PDRs) are
typically dominated by emission from polycyclic aromatic hydrocarbons (PAHs)
and the lowest pure rotational states of molecular hydrogen (H2); two species
which are probes of the physical properties of gas and dust in intense UV
radiation fields. We utilize the high angular resolution of the Infrared
Spectrograph on the Spitzer Space Telescope to construct spectral maps of the
PAH and H2 features for three of the best studied PDRs in the galaxy, NGC 7023,
NGC 2023 and IC 63. We present spatially resolved maps of the physical
properties, including the H2 ortho-to-para ratio, temperature, and G_o/n_H. We
also present evidence for PAH dehydrogenation, which may support theories of H2
formation on PAH surfaces, and a detection of preferential self-shielding of
ortho-H2. All PDRs studied exhibit average temperatures of ~500 - 800K, warm H2
column densities of ~10^20 cm^-2, G_o/n_H ~ 0.1 - 0.8, and ortho-to-para ratios
of ~ 1.8. We find that while the average of each of these properties is
consistent with previous single value measurements of these PDRs, when
available, the addition of spatial resolution yields a diversity of values with
gas temperatures as high as 1500 K, column densities spanning ~ 2 orders of
magnitude, and extreme ortho-to-para ratios of < 1 and > 3.
