We introduce a spectroscopic method that determines nonlinear quantum mechanical response functions beyond the optical diffraction limit and allows direct imaging of nanoscale coherence. In established coherent two-dimensional (2D) spectroscopy, four-wave-mixing responses are measured using three ingoing waves and one outgoing wave; thus, the method is diffraction-limited in spatial resolution. In coherent 2D nanoscopy, we use four ingoing waves and detect the final state via photoemission electron microscopy, which has 50-nanometer spatial resolution. We recorded local nanospectra from a corrugated silver surface and observed subwavelength 2D line shape variations. Plasmonic phase coherence of localized excitations persisted for about 100 femtoseconds and exhibited coherent beats. The observations are best explained by a model in which coupled oscillators lead to Fano-like resonances in the hybridized dark- and bright-mode response.