We report a molecular dynamics study of the interface between water and (macroscopically) water-immiscible room-temperature ionic liquids "ILs", composed of PF6- anions and butyl- versus octyl-substituted methylimidazolium(+) cations (noted BMI+ and OMI+). Because the parameters used to simulate the pure ILs were found to exaggerate the water/IL mixing, they have been modified by scaling down the atomic charges, leading to better agreement with the experiment. The comparison of [OMI][PF6] versus [BMI][PF6] ILs demonstrates the importance of the N-alkyl substituent on the extent of solvent mixing and on the nature of the interface. With the most hydrophobic [OMI][PF6] liquid, the "bulk" IL phase is dryer than with the [BMI][PF6] liquid. At the interface, the OMI+ cations retain direct contacts with the bulk IL, whereas the more hydrophilic PF6 anions gradually dilute in the local water micro-environment and are thus isolated from the "bulk" IL. The interfacial OMI+ cations are ordered with their imidazolium moiety pointing toward the aqueous side and their octyl chains toward the IL side of the interface. With the [BMI][PF6] liquid, the system gradually evolves from an IL-rich to a water-rich medium, leading to an ill-defined interfacial domain with high intersolvent mixing. As a result, the BMI+ cations are isotropically oriented "at the interface". Because the imidazolium cations are more hydrophobic than the PF6- anions, the charge distribution at the interface is heterogeneous, leading to a positive electrostatic potential at the interface with the two studied ILs. Mixing-demixing simulations on [BMI][PF6]/water mixtures are also reported, comparing Ewald versus reaction field treatments of electrostatics. Phase separation is very slow (at least 30 ns), in marked contrast with mixtures involving classical organic liquids, which separate in less than 0.5 ns at the microscopic level. The results allow us to better understand the specificity of the aqueous interfaces with hydrophobic ionic liquids, compared with classical organic solvents, which has important implications as far as the mechanism of liquid-liquid ion extraction is concerned.