Cryogenic scanning tunneling microscopy is used to study local electrical transport properties of thin granular Au/Al2O3 films in the vicinity of the percolation threshold. The current–voltage characteristics are found to vary dramatically from one tip position to another over distances of the order of a few nanometers. The characteristics often exhibit single electron tunneling effects such as the Coulomb blockade and the Coulomb staircase. This behavior is similar to that observed for tunneling into a single isolated nanometer size metallic particle which was explained in terms of a double-barrier tunnel junction model. Some of the characteristics show, however, novel Coulomb-staircase structures having unusual variations in step widths and heights due to complex tunneling paths. A triple-barrier tunnel junction model, where the electron tunnels through two metallic particles along its path, accounts quantitatively for the experimental results.