The structure, energetics, and dynamics of different alkali halide ion pairs hydrated in a hydrophobic medium are studied using molecular dynamics computer simulations. One or two water molecules hydrating NaCl, NaI, KCl, KI, and KF in bulk carbon tetrachloride are considered. The ion pairs remain in contact throughout the simulations, so the structure of the hydration complex is well characterized. The ions' interaction energy and hydration structure are examined and correlated with the ion sizes and charges. For the first four salts, the stronger interaction of the water molecules with the cation than with the anion of the ion pair is in agreement with recent experiments. However, when the anion is significantly smaller than the cation (as in the case of KF, which was not studied experimentally), the opposite behavior is found. The asymmetry of interaction with the cation and the anion are further elucidated by examining hypothetical ion pairs made from equal-sized cations and anions and by defining an asymmetry hydration parameter, which is found to correlate well with the structural characteristics, as well as with the water molecules' reorientation dynamics.