In the semidilute regime, wormlike micelles form an isotropic entangled microstructure that is similar to that of an entangled polymer solution with a characteristic, nanometer-scale entanglement mesh size. We report a combined X-ray photon correlation spectroscopy (XPCS) and rheology study to investigate the translational dynamics of gold nanorods in semidilute solutions of entangled wormlike micelles formed by the surfactant cetylpyridinium chloride (CPyCl) and the counterion sodium salicylate (NaSal). The CPyCl concentration is varied to tune the entanglement mesh size over a range that spans from approximately equal to the nanorod diameter to larger than the nanorod length. The NaSal concentration is varied along with the CPyCl concentration so that the solutions have the maximum viscosity for given CPyCl concentration. On short time scales the nanorods are localized on a length scale matching that expected from the high-frequency elastic modulus of the solutions as long as the mesh size is smaller than the rod length. On longer time scales, the nanorods undergo free diffusion. At the highest CPyCl concentrations, the nanorod diffusivity approaches the value expected based on the macroscopic viscosity of the solutions, but it increases with decreasing CPyCl concentration more rapidly than expected from the macroscopic viscosity. A recent model by Cai et al. [Cai, L.-H.; Panyukov, S.; Rubinstein, M. Macromolecules 2015, 48, 847-862] for nanoparticle "hopping" diffusion in entangled polymer solutions accounts quantitatively for this enhanced diffusivity.