A plasmonic nanostructure (PNS) which integrates metallic and dielectric media within a single structure has been shown to exhibit specific plasmonic properties which are considered useful in refractive index (RI) sensor applications. In this paper, the simultaneous realization of sensitivity and tunability of the optical properties of PNSs consisting of alternative Ag and dielectric of nanosphere/nanorod array have been proposed and compared by using three-dimensional finite element method. The proposed system can support plasmonic hybrid modes and the localized surface plasmonic resonances and cavity plasmonic resonances within the individual PNS can be excited by the incident light. The proposed PNSs can be operated as RI sensor with a sensitivity of 500 nm/RIU (RIU = refractive index unit) ranging from UV to the near-infrared. In addition, a narrow bandwidth and nearly zero transmittance along with a high absorptance can be achieved by a denser PNSs configuration in the unit cell of PNS arrays. We have demonstrated the number of modes sustained in the PNS system, as well as, the near-field distribution can be tailored by the dielectric media in PNSs.