As materials approach the atomically-thin limit, the effect of surfaces on electronic properties becomes increasingly important. Surfaces can exhibit unusual atomic and electronic structures, which can be drastically different than those observed in bulk materials. Scanning tunneling microscopy/spectroscopy (STM/STS) is an important tool for studying this, enabling direct visualization of atomic and electronic structures at surfaces. Using STM/STS we have studied atomically-thin RbI, which serves as a model system for strong substrate/adlayer coupling on metal surfaces. This strong coupling leads to unexpected atomic structures and intriguing electronic states which are localized to the surface. Furthermore, RbI shows surprisingly strong interactions with adsorbate nanostructures, leading to significant modulation in the electronic structure of adsorbed single-walled carbon nanotubes.