In this work, we use molecular dynamics simulations to investigate the hydrodynamics in dilute suspensions of nanoparticles. Both the nanoparticle and the solvent are represented explicitly using detailed molecular models. Diffusion and hydrodynamics are governed by the intermolecular interactions in such a model system. We track the motion of nanoparticles in the solvent and near a solid surface and monitor their velocity, friction and normal forces. The applicability of the Stokes law at the nanoscale is assessed and the conditions that lead to deviations from it are identified. Furthermore, both the interactions between neighboring particles in a suspension and the effect of the solid surface on the hydrodynamic interactions are investigated in detail. Simulation results are compared with continuum mechanics predictions and the observed deviations are explained using the molecular level structure in the system.