Cosmic ray transport on galactic scales depends on the detailed properties of the magnetized, multiphase interstellar medium (ISM). In this work, we post-process a high-resolution TIGRESS magnetohydrodynamic simulation modeling a local galactic disk patch with a two-moment fluid algorithm for cosmic ray transport. We consider a variety of prescriptions for the cosmic rays, from a simple purely diffusive formalism with constant scattering coefficient, to a physically-motivated model in which the scattering coefficient is set by critical balance between streaming-driven Alfven wave excitation and damping mediated by local gas properties. We separately focus on cosmic rays with kinetic energies of $sim 1$ GeV (high-energy) and $sim 30$~MeV (low-energy), respectively important for ISM dynamics and chemistry. We find that simultaneously accounting for advection, streaming, and diffusion of cosmic rays is crucial for properly modeling their transport. Advection dominates in the high-velocity, low-density, hot phase, while diffusion and streaming are more important in higher density, cooler phases. Our physically-motivated model shows that there is no single diffusivity for cosmic-ray transport: the scattering coefficient varies by four or more orders of magnitude, maximal at density $n_mathrm{H} sim 0.01, mathrm{cm}^{-3}$. Ion-neutral damping of Alfven waves results in strong diffusion and nearly uniform cosmic ray pressure within most of the mass of the ISM. However, cosmic rays are trapped near the disk midplane by the higher scattering rate in the surrounding lower-density, higher-ionization gas. The transport of high-energy cosmic rays differs from that of low-energy cosmic rays, with less effective diffusion and greater energy losses for the latter.
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