Coherent phonon spectroscopy can provide microscopic insight into ultrafast lattice dynamics and its coupling to other degrees of freedom under nonequilibrium conditions. Ultrafast optical spectroscopy is a well-established method to study coherent phonons, but the diffraction limit has hampered observing their local dynamics directly. Here, we demonstrate nanoscale coherent phonon spectroscopy using ultrafast laser-induced scanning tunneling microscopy in a plasmonic junction. Coherent phonons are locally excited in ultrathin zinc oxide films by the tightly confined plasmonic field and are probed via the photoinduced tunneling current through an electronic resonance of the zinc oxide film. Concurrently performed tip-enhanced Raman spectroscopy allows us to identify the involved phonon modes. In contrast to the Raman spectra, the phonon dynamics observed in coherent phonon spectroscopy exhibit strong nanoscale spatial variations that are correlated with the distribution of the electronic local density of states resolved by scanning tunneling spectroscopy.