Reproducing the spatial and kinematic distribution of satellite dwarf galaxies in the Local Group (LG) is an important test of both physical models and numerical resolution in simulations. Using the FIRE-2 cosmological zoom-in baryonic simulations, we examine the radial distributions of satellites with stellar masses of at least 105 Msun around 14 Milky Way (MW) and Andromeda (M31)-like host galaxies. We find excellent agreement with the inner radial profiles of the MW and M31, and our results suggest more undiscovered classical dwarf-mass satellites in the LG. We also examine the 3D spatial distribution and kinematics of LG satellites in the context of satellite planes. Simulated satellites are usually distributed nearly isotropically around their hosts, but there are a few systems whose satellite populations lie within thin planes. We find that hosts with an LMC-like satellite near first pericenter are more likely to have MW-like satellite planes that are also longer-lived, likely because of group accretion of satellites.