Ion-specific solvation has fundamental implications in biochemistry, and the thermodynamics and dynamics of aqueous salt solutions have correspondingly been investigated intensively. Nonetheless, there are fundamental unresolved issues in modeling the dynamics of aqueous salt solutions and the related problem of polymers dissolved in these solutions. In particular, experiments show that the self-diffusion coefficient, D, of water molecules in electrolyte solutions can be either enhanced or suppressed by particular salts having the same valence where the observed changes correlate with the Hofmeister series governing the relative solubility of proteins and water-soluble polymers in the same salt solutions. Recent studies have demonstrated that common atomistic models of aqueous electrolyte solutions completely fail to reproduce this basic phenomenon. Drawing on similar trends observed in the field of polymer nanocomposites, we propose a coarse-grained model of aqueous electrolyte solutions that captures the observed trends and that offers physical insight into the influence of salt on the thermodynamic and dynamic properties of electrolyte solutions.