We report scanning tunneling microscopy results on 25- and 50-nm-thick films of superconducting TiN that show Andreev tunneling behavior at 0.5 K. At most locations on the topographically rough surfaces, we observe tip-sample current-voltage characteristics with a clear superconducting gap, as expected for superconductor-normal (S-N) tunneling through a low-transparency barrier, while in some places, we find a zero-voltage conductance peak, as expected for S-N Andreev tunneling through a highly transparent barrier. Fitting the Blonder-Tinkham-Klapwijk model to the conductance data allows an accurate extraction of the TiN superconducting gap Delta, by accounting for local variations in the tip-sample barrier height Z and junction temperature T. From spatial maps of the model parameters, we find that both films show a strong inhomogeneity, with Delta varying by as much as a factor of 2 from grain to grain. In the thicker film, however, correlations between T, Z, and Delta suggest the grains are thermally isolated, perhaps due to internal stress. We discuss possible mechanisms that could produce these large correlated variations, including local heating and surface contamination, and consider some of the implications for devices made from such films.