Drought is one of the most complex and poorly understood catastrophes on the planet. Between the Greek mainland and Turkey, there is an area of Greece known as the South Aegean Islands, that experiences water supply issues. As a result, there are issues related to the socioeconomic growth of some of these islands, and the need for water transportation by water vessels. Water transportation by ships to the Cyclades and Dodecanese areas from the mainland or other adjacent islands to satisfy urgent demands, on the other hand, is exceptionally expensive. The situation deteriorates during the summer, when drinking water needs can reach five times the norm, due to the heavy tourist season. Given these conditions, the aim of this research is to estimate hydrometeorological conditions, calculate the water balance, and determine water needs in three southern Aegean islands (Mykonos, Naxos, and Kos), where there is a water shortage, particularly during the summer months when tourism activity is at its peak. The modified Thornthwaite–Mather monthly hydrological balance model was applied to determine the water balance. Various water use datasets (drinking water, irrigation, water transportation) were employed to quantify the water demands in the three islands. According to the results, the available water (runoff + infiltration) seems to be more than sufficient to meet the needs of the islands of Naxos and Kos, since it far exceeds the increased needs of the islands. Yet, it appears that in Mykonos, where the water resources have been nearly entirely utilized, the available water, is just enough to meet the water needs. It is evident that all three islands present significant sources of available water, which could meet the growing needs of the residents. However, the absence of the necessary water exploitation projects, mainly concerning the surface runoff, has contributed to the intense water supply problems of the islands. The importance of the water harvesting projects becomes even more urgent under the conditions of climate change, with the decrease in annual rainfall likely to be a highly possible scenario, especially in arid and semi-arid regions.