The cold neutral medium (CNM) is an important part of the galactic gas cycle and a precondition for the formation of molecular and star-forming gas, yet its distribution is still not fully understood. In this work, we present extremely high resolution simulations of spiral galaxies with time-dependent chemistry such that we can track the formation of the CNM, its distribution within the galaxy, and its correlation with star formation. We find no strong radial dependence between the CNM fraction and total neutral atomic hydrogen (H i) due to the decreasing interstellar radiation field counterbalancing the decreasing gas column density at larger galactic radii. However, the CNM fraction does increase in spiral arms where the CNM distribution is clumpy, rather than continuous, overlapping more closely with H-2. The CNM does not extend out radially as far as H i, and the vertical scale height is smaller in the outer galaxy compared to H i with no flaring. The CNM column density scales with total mid-plane pressure and disappears from the gas phase below values of P-T/k(B) = 1000 K cm(-3). We find that the star formation rate density follows a similar scaling law with CNM column density to the total gas Kennicutt-Schmidt law. In the outer galaxy, we produce realistic vertical velocity dispersions in the H i purely from galactic dynamics, but our models do not predict CNM at the extremely large radii observed in H i absorption studies of the Milky Way. We suggest that extended spiral arms might produce isolated clumps of CNM at these radii.