The availability of groundwater is of concern. The demand for groundwater in Korea increased by more than 100% during the period 1994–2014. This problem will increase with population growth. Thus, a reliable groundwater analysis model for regional scale studies is needed. This study used the geographical information system (GIS) data and machine learning to map groundwater potential in Gangneung-si, South Korea. A spatial correlation performed using the frequency ratio was applied to determine the relationships between groundwater productivity (transmissivity data from 285 wells) and various factors. This study used four topography factors, four hydrological factors, and three geological factors, along with the normalized difference wetness index and land use and soil type. Support vector regression (SVR) and metaheuristic optimization algorithms—namely, grey wolf optimization (GWO), and particle swarm optimization (PSO), were used in the construction of the groundwater potential map. Model validation based on the area under the receiver operating curve (AUC) was used to determine model accuracy. The AUC values of groundwater potential maps made using the SVR, SVR_GWO, and SVR_PSO algorithms were 0.803, 0.878, and 0.814, respectively. Thus, the application of optimization algorithms increased model accuracy compared to the standard SVR algorithm. The findings of this study improve our understanding of groundwater potential in a given area and could be useful for policymakers aiming to manage water resources in the future.