We used 3.6, 8.0, 70, 160 micron Spitzer Space Telescope data, James Clerk Maxwell Telescope HARP-B CO J=(3-2) data, National Radio Astronomy Observatory 12 meter telescope CO J=(1-0) data, and Very Large Array HI data to investigate the relations among PAHs, cold (~20 K) dust, molecular gas, and atomic gas within NGC 2403, an SABcd galaxy at a distance of 3.13 Mpc. The dust surface density is mainly a function of the total (atomic and molecular) gas surface density and galactocentric radius. The gas-to-dust ratio monotonically increases with radius, varying from ~100 in the nucleus to ~400 at 5.5 kpc. The slope of the gas-to-dust ratio is close to that of the oxygen abundance, suggesting that metallicity strongly affects the gas-to-dust ratio within this galaxy. The exponential scale length of the radial profile for the CO J=(3-2) emission is statistically identical to the scale length for the stellar continuum-subtracted 8 micron (PAH 8 micron) emission. However, CO J=(3-2) and PAH 8 micron surface brightnesses appear uncorrelated when examining sub-kpc sized regions.