Clusters containing the K+or Cl-ion at the centre with 14 or 26 water molecules are investigated by means of computer experiments. For two models of water, the profiles for atomic density, the local energy per molecule, the normal component of the pressure tensor, the polarization vector, the volume and molecular polarizabilities, the local electric potential and the electric field affecting a water molecule are obtained. The most probable configurations of water molecules in the hydration shells are studied in detail. The lifetime τ of a molecule in the first hydration shell and the coefficients of the normal (transversal),DN, and tangential (longitudinal),DT, self-diffusion are estimated. The size dependence of the cluster properties is considered. The grand potential of a liquid cluster around an ion is calculated. The thermodynamic conclusion regarding the difference in the work of formation of clusters on oppositely charged cores is verified.