The diffraction of core-level photoelectrons in local atomic clusters leads to pronounced intensity anisotropies in the corresponding photoemission signals from single crystalline surfaces. The resulting emission patterns contain detailed structural information of the environment of the photoemitting atom. In the case of surface-supported nanostructures, core levels of different elements can be selected in order to probe the local structure around the different constituents. The combination with scanning tunneling microscopy data, showing the distribution, size and shape of the nano-objects, proves to be very interesting. Three case studies illustrate the kind of information that is available from this combined nano-analysis: molecular orientation in well-ordered chains of C60 molecules on a vicinal Cu(111) surface, the atomic structure of line defects in epitaxial monolayers of hexagonal boron nitride (h-BN) on Ni(111), and the structural characterization of two orthogonal one-dimensional h-BN and boron phases grown on Mo(110).