  We study the sensitivity of detectors with directional sensitivity to
coherent elastic neutrino-nucleus scattering (CE$\nu$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 $\sim 50$ keV. Combined with energy and
timing information, directional information can play an important role in
extracting new physics from CE$\nu$NS experiments.
