The local structural and electronic properties of individual metallofullerenes are studied using scanning tunneling microscopy, scanning tunneling spectroscopy, and theoretical simulations. The energy-resolved metal-cage hybrid states of a single endohedral metallofullerene Dy@C82 isomer I have been spatially mapped, supporting a complex picture consisting of the orbital hybridization and charge transfer for the interaction between the cage and the metal atom. The relative position of the encapsulated Dy atom inside the cage and the molecular orientation on the surface have been inferred by comparing the experimental results with theoretical simulations. The combined technique provides promising applications in the fields of in situ characterization and diagnostics of metallofullerene-based nanodevices.