Local variations of superconductivity have been studied using scanning tunneling microscopy around nano-cavities formed by Ar ions embedded in Pb(111). Various factors including the density of states at Fermi energy, electron-phonon couplings, and quantum well states, which are known to affect superconductivity, have been examined. We show that the superconductivity is enhanced near the nano-cavities and propose that quantum effects such as quantum confinement, proximity effect and multi-gap effect are possibly involved in determining the superconducting gap of this system. These results have important implications for the characterization and understanding of superconductivity at a nanometer scale.