Aqueous ionic solutions are ubiquitous in chemistry and in biology. Experiments show that ions affect water dynamics, but a full understanding of several questions remains needed: why some salts accelerate water dynamics while others slow it down, why the effect of a given salt can be concentration-dependent, whether the effect of ions is rather local or more global. Numerical simulations are particularly suited to disentangle these different effects, but current force fields suffer from limitations and often lead to a poor description of dynamics in several aqueous salt solutions. Here, we develop an improved classical force field for the description of alkali halides that yields dynamics in excellent agreement with experimental measurements for water reorientational and translational dynamics. These simulations are analyzed with an extended jump model, which allows to compare the effects of ions on local hydrogen-bond exchange dynamics and on more global properties like viscosity. Our results unambiguously show that the ion-induced changes in water dynamics are usually mostly due to a local effect on the hydrogen-bond exchange dynamics; in contrast, the change in viscosity leads to a smaller effect, which governs the retardation only for a minority of salts and at high concentrations. We finally show how the respective importance of these two effects can be directly determined from experimental measurements alone, thus providing guidelines for the selection of an electrolyte with specific dynamical properties.