Molecular dynamics simulations of mixtures of 1,3-dialkyl imidazolium ionic liquids and water have been performed in order to investigate the microscopic physical properties as a function of composition. The behavior of two ionic liquids has been compared, namely 1,3-dimethylimidazolium chloride and 1,3-dimethylimidazolium hexafluorophosphate. The hexafluorophosphate ionic liquids are known to be more hydrophobic as solvents than the corresponding chloride liquids. This is manifested in our simulations by differences in the signs of both the excess volumes and the enthalpies of mixing. However, there is surprisingly little difference in the microscopic properties. In both liquids, water molecules tend to be isolated from each other in mixtures with more ions than water molecules. When the molar proportion of water molecules reaches 75%, a percolating network of waters is found as well as some isolated molecules and small clusters. In all cases, molecular motion becomes faster as the proportion of water increases, although there are some differences in the details of the translational and rotational motion.