Surface plasmon (SP) technologies exploit the spectral and spatial properties of collective electronic oscillations in noble metals placed in an incident optical field. Yet the SP local density of states (LDOS), which rule the energy transducing phenomena between the SP and the electromagnetic field, is much less exploited. Here, we use two-photon luminescence (TPL) microscopy to reveal the SP-LDOS in thin single-crystalline triangular gold nanoprisms produced by a quantitative one-pot synthesis at room temperature. Variations of the polarization and the wavelength of the incident light redistribute the TPL intensity into two-dimensional plasmonic resonator patterns that are faithfully reproduced by theoretical simulations. We demonstrate that experimental TPL maps can be considered as the convolution of the SP-LDOS with the diffraction-limited Gaussian light beam. Finally, the SP modal distribution is tuned by the spatial coupling of nanoprisms, thus allowing a new modal design of plasmonic information processing devices.