In this study, the dispersion behavior of piezoelectric sandwich nanoplates is examined using the nonlocal strain gradient theory (NSGT). Specifically, the evolution law of frequency and phase velocity (PV) with the wave number (WN) is investigated. The sandwich nanoplate has a metallic central layer and a piezoelectric surface layer, and the nanoplate is deposited on top of a viscoelastic substrate. The viscoelastic substrate is modeled using a three-parameter viscoelastic model. The surface effects (SEs) of the piezoelectric layer, including its elastic parameters, piezoelectric parameters, dielectric parameters, and residual stresses, on the dispersion characteristics are systematically considered. The equations of motion are determined by Hamilton's principle and NSGT. Furthermore, the scale effects, SEs, and viscoelastic effects on the dispersion properties are comprehensively explored. The results reveal that the contribution of scale and viscoelastic effects to the dispersion properties is strongly dependent on the WN, and the impact of SEs on the frequency is inseparable from the thickness of the piezoelectric sandwich nanoplates.