The effect of ions on the properties of aqueous solutions is often categorized in terms of the Hoftneister series that ranks them from chaotropes ("structure-breakers"), which weaken the surrounding hydrogen-bond network to kosmotropes ("structure-makers"), which enhance it. Here, we investigate the Hofmeister series in similar to 1 M sodium-halide solutions using molecular dynamics simulations to calculate the effect of the identity and proximity of the halide anion on both the water diffusion coefficient and its activation energy. A recently developed method for calculating the activation energy from a single-temperature simulation is used, which also permits a rigorous decomposition into contributions from different interactions and motions. The mechanisms of the salt effects on the water dynamics are explored by separately considering water molecules based on their location relative to the ions. The results show that water diffusion is accelerated moving down the halide group from F- to I-. The behavior of the diffusion activation energy, E-a is more complex, indicating a significant role for entropic effects. However, water molecules in the first or second solvation shell of an ion exhibit a decrease in E-a moving down the halide series and Na+ exhibits a larger effect than any of the anions. The E(a )for water molecules within the second solvation shell of an ion are modest, indicating a short-ranged nature of the ion influence.