Plasmonic nanostructures are versatile tools for coupling electromagnetic waves to electronic charge oscillations in noble metals at sub-wavelength length scales. The plasmon resonance frequencies of a noble metal depend on its geometry and refractive index of the material, making them ideal nanosensors for local detection of mechanical vibrations and acoustic waves. In this work, we present a pillar-based plasmonic architecture comprised of an array of gold dimers elevated from the substrate by narrow polymer or silica posts that enable efficient funneling of far-field light to plasmons in the gap between the gold dimers, with limited coupling to the substrate. The localized gap plasmon resonance of a coupled gold dimer is strongly modulated by width of the nanoscale gap separating the gold caps, as such, the nanomechanical vibration of the caps is readout by the demodulation of the intensity of the far-field optical scattering. In this work, we explore the gold dimers to demonstrate polarization sensitive detection of in-plane nanomechanical vibrations at frequencies of up 20 GHz in various dimer configurations. We explore numerical modeling to quantify the displacement sensitivity of the plasmonic-nanomechanical device and to investigate the dependence of the vibration detection sensitivity on the dimer configurations. This work may has the potential to pave the way for developing pillar plasmonic dimers for high frequency nanomechanical sensing and ultrafast reconfigurable photonic devices based on coupled plasmonic oscillators and GHz nanomechanical resonators.