Metallic nanoparticles are known to exhibit strong particle size dependent localized surface plasmon resonances due to their specific optical response described via the complex dielectric function. Using the two-dimensional finite element method, the near-field behavior of core-shell nanocylinder dimers with either a dielectric or a gold core and a silver shell was investigated. With a detailed analysis the positions of maximum field enhancement usable for highly sensitive spectroscopy were unveiled and the surface charge distributions of the different kinds of resonances were visualized. It is shown that the usual far-field spectra do not give reliable estimates of local electric field peaks. Furthermore one observes a distinct mode at the natural plasma frequency of the silver shell which is independent of the core material. This mode is identified as a volume plasmon mode.