By using scanning tunneling microscopy/spectroscopy we show that the interface between LaAlO3 and SrTiO3 band insulators is characterized by in-gap interface states. These features were observed in insulating as well as conducting LaAlO3/SrTiO3 bilayers. The data show how the interface density of states evolves across the insulating to metal transition, demonstrating that nanoscale electronic inhomogeneities in the system are induced by spatially localized electrons.