Plasmonic structures couple oscillating electromagnetic fields to conduction electrons in noble metals and thereby can confine optical-frequency excitations at nanometre scales. This confinement both facilitates miniaturization of nanophotonic devices and makes their response highly sensitive to mechanical motion. Mechanically coupled plasmonic devices thus hold great promise as building blocks for next-generation reconfigurable optics and metasurfaces. However, a flexible approach for accurately batch-fabricating high-performance plasmomechanical devices is currently lacking. Here we introduce an architecture integrating individual plasmonic structures with precise, nanometre features into tunable mechanical resonators. The localized gap plasmon resonators strongly couple light and mechanical motion within a three-dimensional, sub-diffraction volume, yielding large quality factors and record optomechanical coupling strength of 2 THz center dot nm(-1). Utilizing these features, we demonstrate sensitive and spatially localized optical transduction of mechanical motion with a noise floor of 6 fm center dot Hz(-1/2), representing a 1.5 orders of magnitude improvement over existing localized plasmomechanical systems.