Microscopic dynamics of plasmonic systems characterized by sub-nanometer gaps can be crucial to accurately describe their macroscopic optical properties. First-principle quantum mechanical approaches, such as Time-Dependent Density Functional Theory (TD-DFT), can give a very good approximation although their applicability is often limited to very small systems due to computational costs. Quantum hydrodynamic theory (QHT) is a promising tool which can efficiently predict the optical response of multiscale plasmonic systems. We apply this theory to investigate plasmonic response of spherical nanomatryoshkas (NMs), which are concentric core-shell structures, for Au and Na metals in the quantum tunneling regime. The results obtained for Au NMs are in a very good agreement with those of TD-DFT, already reported in the literature. We also study optical properties of quite big systems, both for Au and Na, whose sizes make them inaccessible for DFT calculations. We analyze the impact of core-shell spacing on near-field and far-field optical behavior of these systems and find that the QHT method predicts the nonlocal and quantum effects in multiscale plasmonic systems in an efficient manner. A systematic comparison between the local response, Thomas-Fermi and QHT approximations has also been presented. The results show that as the core-shell distance decreases the nonlocal or quantum effects strongly influence the plasmonic properties of these systems which can be nicely described by the QHT. For numerical implementation of these structures, we fully exploit the symmetry of the geometry and use a 2.5D simulation technique which reduces the computational efforts to a great extent.