The properties of glasses vary widely depending on the way they are prepared, even though their structures appear similar. We show that the local potential energy landscape (PEL) sensitively reflects the stability differences through simulation of local structural excitation in a model metallic glass. It is observed that the spectrum of local structural excitation develops a pseudogap at low energies as the glass becomes more stable. We also demonstrate that the spatial variation of the atomic level shear modulus, rather than the distribution of the magnitude of the single atom shear modulus, is more closely related to the nature of the PEL and the stabilities of glasses. In particular, local aggregation of atoms with low shear modulus greatly contributes to instability of the system.