Nanorod diffusion and polymer dynamics in nano-composites were investigated by means of molecular dynamics simulations. We show that thin nanorods (spherocylinders) can diffuse much faster than that predicted by a Stokes-Einstein continuum model, similar to experiments, in the dilute nanorod regime. In entangled polymer matrices, nanorod diffusion reaches a plateau region. Increase of the nanorod diameter or aspect ratio (AR) slows its diffusion. The nanorod diffusion, at long time scales, displays a non-Gaussian behavior as is depicted by the several Gaussian peaks present in the self-part of the van Hove function. We also show that the unentangled polymer dynamics decreases in the nanocomposite due to the nanorods interfacial area.