Using scanning tunneling microscopy and density functional theory (DFT), we have analyzed the local electronic properties of (111)-oriented MgO nanoislands on Au(111). Conductance and barrier-height measurements revealed substantial modulations in the electronic structure and electrostatic potential across the islands, with particularly high and low values for band onsets and surface potential occurring at the perimeter and in the island center, respectively. DFT calculations showed that MgO(111) monolayer structures exhibit a strongly reduced distance between the Mg delta(+) and O delta- plane as compared to bulk MgO, which in turn suppresses the polar character of the film. The spatial modulations in the electronic properties originate from gradual changes of the interface registry when approaching the island edges, driven by a small mismatch between the Au(111) and MgO(111) lattices. At the periphery of the islands, additional effects such as band shifts and low-lying electronic states are observed, which arise from the interplay of residual edge polarity and unsaturated chemical bonds. We expect that the peculiar edge properties of MgO(111) islands are decisive for the chemical behavior of the nanostructures.