Potable water and power shortage are major concerns for the world community. Large-scale energy storage systems (ESSs) are a suitable solution for grid-scale energy storage, among which Compressed air energy storage (CAES) is a lead technology. Hybrid CAES-Desalination was introduced in previous investigations. The system can supply power and potable water simultaneously which can be a strategic system for dry and warm climates. Multi-stage flash (MSF) and multi-effect distillation (MED) are modeled and thoroughly investigated in this paper. The CAES system's exhaust hot air is the drive power of the distillation systems. Therefore, not only the CAES system's performance is improved but also a large amount of drinkable water is generated. The compressors and turbine's dissipated heat play as the main sources in the distillation unit in charging and discharging periods, respectively. This paper has mainly focused on the exergy and economic analyses of this integration and has worked on the optimum arrangement considering exergy and economic investigation. This paper has also studied the exergy and economic analyses of the CAES system's recuperator removal. The exergy analysis declares that the majority of the exergy destruction in desalination units happens at the first stage where the heat exchange occurs. It also shows that pressure regulator, HTES, and turbine are responsible for significant shares of exergy destruction in the CAES system. The economic assessment expresses 5.1 years for the payback time of the integrated system.