Metal nanoparticles are attractive for plasmon enhanced generation of hot carriers, which may be harnessed in photochemical reactions. In this work, we analyze the coherent femtosecond dynamics of photon absorption, plasmon formation, and subsequent hot-carrier generation via plasmon dephasing using first-principles simulations. We predict the energetic and spatial hot-carrier distributions in small metal nanoparticles and show that the distribution of hot electrons is very sensitive to the local structure. Our results show that surface sites exhibit enhanced hot-electron generation in comparison to the bulk of the nanoparticle. While the details of the distribution depend on particle size and shape, as a general trend lower-coordinated surface sites (e.g., corners, edges, 100 facets) exhibit a higher proportion of hot electrons than higher-coordinated surface sites (e.g., 111 facets). The present results thereby demonstrate how hot-carrier distributions can be tailored by careful design of particle size, structure, and composition.