We have measured the energies, relative intensities, and spatial distribution of deep level defect transitions near GaN/InGaN/GaN quantum well structures using low-energy electron-excited nanoscale-luminescence (LEEN) spectroscopy. Results obtained with electron excitation energies as low as 100 eV provide evidence on an incremental, 10-20 nm scale for defects within the GaN confinement layer, their variation with distance from the quantum well, and their electronic quality relative to the GaN substrate. The InGaN quantum well and GaN near-band-edge luminescence intensities exhibit strong variations as a function of excitation depth. Combined with a model of energy-dependent penetration, diffusion, and recombination, these variations indicate a value of 25-28 nm for the minority carrier diffusion length within the GaN confinement layer. Depth-dependent spectra also reveal the presence of cubic GaN phase formation at the InGaN/GaN substrate interface of a relatively In-rich quantum well structure. The contrast in LEEN features between structures of two different InGaN quantum well compositions demonstrates the effect of growth composition on local state formation.