The intense local field induced near metallic nanostructures that provides strong enhancements for surface enhanced spectroscopies has been a major focus of plasmonics research over the past decade. However, plasmonic nanoparticles can also induce remarkably large electromagnetic field gradients near their surfaces. Sizeable field gradients can excite dipole-forbidden transitions in nearby atoms or molecules and provide unique spectroscopic fingerprinting for chemical and bimolecular sensing. Here we investigate how the local field gradients near metallic nanostructures depend on geometry, polarization, and wavelength. We introduce the concept of the Local Angular Momentum (LAM) vector as a useful figure of merit for the design of nanostructures that provide large field gradients. This quantity, based on integrated fields rather than field gradients, is particularly well suited for optimization using numerical grid-based full wave electromagnetic simulations. The LAM vector has a more compact structure than the gradient matrix and can be straightforwardly associated with the angular momentum of the electromagnetic fields incident on the plasmonic structures.