Argon-filled nanocavities embedded in a single crystal of copper near the surface reflect electrons and induce a quantum well (QW) between the nanocavity and the atomically flat Cu(001) surface. The spatial variation of conductance at the surface above the nanocavity was studied by scanning tunnelling microscopy and/or spectroscopy. Interference features were observed over several nanometers at some locations on the surface. In the  and  directions, the interference fringes propagate over longer distances up to tens of nanometers. In addition to these spatially resolved features, the conductance reveals an oscillatory behavior as a function of energy of injected electrons. A model taking into account the specific shape of the nanocavity, as well as the band structure of copper, allows us to simulate the spatial variation of the conductance in close agreement with the experiment. The modeling demonstrates that not only the specific shape of the subsurface nanocavity reflecting electrons is crucial to explain the observed pattern, but also the anisotropy of the band structure and the phenomenon of focusing of hot electrons connected to it. Our approach opens up opportunities to examine buried nano-objects with scanning tunneling microscopy, and also to study how the anisotropy of a crystal influences the spatial variation of QW properties.