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CO is the most widely used observational tracer of molecular gas. The observable CO luminosity is translated to H_2 mass via a conversion factor, X_CO, which is a source of uncertainty and bias. Despite variations in X_CO, the empirically-determined solar neighborhood value is often applied across different galactic environments. To improve understanding of X_CO, we employ 3D magnetohydrodynamics simulations of the interstellar medium (ISM) in galactic disks with a large range of gas surface densities, allowing for varying metallicity, far-ultraviolet (FUV) radiation, and cosmic ray ionization rate (CRIR). With the TIGRESS simulation framework we model the three-phase ISM with self-consistent star formation and feedback, and post-process outputs with chemistry and radiation transfer to generate synthetic CO(1--0) and (2--1) maps. Our models reproduce the observed CO excitation temperatures, line-widths, and line ratios in nearby disk galaxies. X_CO decreases with increasing metallicity, with a power-law slope of -0.8 for the (1--0) line and -0.5 for the (2--1) line. X_CO also decreases at higher CRIR, and is insensitive to the FUV radiation. As density increases, X_CO first decreases due to increasing excitation temperature, and then increases when the emission is fully saturated. We provide fits between X_CO and observable quantities such as the line ratio, peak antenna temperature, and line brightness, which probe local gas conditions. These fits, which allow for varying beam size, may be used in observations to calibrate out systematic biases. We also provide estimates of the CO-dark H_2 fraction at different gas surface densities, observational sensitivities, and beam sizes.