We study the sensitivity of detectors with directional sensitivity to coherent elastic neutrino-nucleus scattering (CE.NS), and how these detectors complement measurements of the nuclear recoil energy. We consider stopped pion and reactor neutrino sources, and use gaseous helium and fluorine as examples of detector material. We generate Standard Model predictions, and compare to scenarios that include new, light vector or scalar mediators. We show that directional detectors can provide valuable additional information in discerning new physics, and we identify prominent spectral features in both the angular and the recoil energy spectrum for light mediators, even for nuclear recoil energy thresholds as high as similar to 50 keV. Combined with energy and timing information, directional information can play an important role in extracting new physics from CE.NS experiments.