We used Spitzer Space Telescope 3.6, 8.0, 70 and 160μm data, James Clerk Maxwell Telescope HARP-B CO J = (3-2) data, National Radio Astronomy Observatory 12 m telescope CO J = (1-0) data and Very Large Array HI data to investigate the relations among polycyclic aromatic hydrocarbons (PAHs), cold (~20K) dust, molecular gas and atomic gas within NGC 2403, an SABcd galaxy at a distance of 3.13Mpc. 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 5.5kpc. 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 8μm (PAH 8μm) emission. However, CO J = (3-2) and PAH 8μm surface brightnesses appear uncorrelated when examining sub-kpc-sized regions.