We present kiloparsec (kpc) spatial resolution maps of the CO-to-H2 conversion factor (alpha_co) and dust-to-gas ratio (DGR) in 26 nearby, star-forming galaxies. We have simultaneously solved for alpha_co and DGR by assuming that the DGR is approximately constant on kpc scales. With this assumption, we can combine maps of dust mass surface density, CO integrated intensity and HI column density to solve for both alpha_co and DGR with no assumptions about their value or dependence on metallicity or other parameters. Such a study has just become possible with the availability of high resolution far-IR maps from the Herschel key program KINGFISH, 12CO J=(2-1) maps from the IRAM 30m large program HERACLES and HI 21-cm line maps from THINGS. We use a fixed ratio between the (2-1) and (1-0) lines to present our alpha_co results on the more typically used 12CO J=(1-0) scale and show using literature measurements that variations in the line ratio do not effect our results. In total, we derive 782 individual solutions for alpha_co and DGR. On average, alpha_co = 3.1 Msun pc^-2 (K km s^-1)^-1 for our sample with a standard deviation of 0.3 dex. Within galaxies we observe a generally flat profile of alpha_co as a function of galactocentric radius. However, most galaxies exhibit a lower alpha_co in the central kpc---a factor of ~2 below the galaxy mean, on average. In some cases, the central alpha_co value can be factors of 5 to 10 below the standard Milky Way (MW) value of alpha_co,MW =4.4 Msun pc^-2 (K km s^-1)^-1. While for alpha_co we find only weak correlations with metallicity, DGR is well-correlated with metallicity, with an approximately linear slope. Finally, we present several recommendations for choosing an appropriate alpha_co for studies of nearby galaxies.
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