We investigate the reorientation dynamics of water at 300 K in solutions of magnesium sulfate and cesium chloride from classical atomistic molecular dynamics simulations using the "simple water model with four sites and negative Drude polarizability" (SWM4-NDP) and accompanying ion models; for SO4(2-), we derive SWM4-NDP-compatible parameters. Results indicate that pairs of ions have a cooperative effect on water rotation but do not support the model based on experiment whereby ion cooperativity increases the number of very slow water molecules well beyond the ions' first hydration shell. Instead, we find that cooperative slowdown beyond the first hydration shell is weak. Intense cooperative slowdown is limited to the first hydration shells, the magnitude of the slowdown being stronger for the multivalent ions. Cooperative effects for different salts differ in both the magnitude of rotational slowdown and the spatial range of the affected water subpopulations.