Continuous generation of radon gas by soil and rocks rich in components of the uranium chain, along with prolonged inhalation of radon progeny in enclosed spaces, can lead to severe respiratory diseases. Detection of radon-prone areas and acquisition of detailed knowledge regarding relationships between indoor radon variations and geogenic factors can facilitate the implementation of more appropriate radon mitigation strategies in high-risk residential zones. In the present study, 10 factors (i.e., lithology; fault density; mean soil calcium oxide [CaO], copper [Cu], lead [Pb], and ferric oxide [Fe2O3] concentrations; elevation; slope; valley depth; and the topographic wetness index [TWI]) were selected to map radon potential areas based on measurements of indoor radon levels in 1,452 dwellings. Mapping was performed using three machine learning methods: long short-term memory (LSTM), extreme learning machine (ELM), and random vector functional link (RVFL). The results were validated in terms of the area under the receiver operating characteristic curve (AUROC), root mean square error (RMSE), and standard deviation (StD). The prediction abilities of all models were satisfactory; however, the ELM model had the best performance, with AUROC, RMSE, and StD values of 0.824, 0.209, and 0.207, respectively. Moreover, approximately 40% of the study area was covered by very high and high-risk radon potential zones that mainly included populated areas in Danyang-gun, South Korea. Therefore, the map can be used to establish more appropriate construction regulations in radon-priority areas, and identify more cost-effective remedial actions for existing buildings, thus reducing indoor radon levels and, by extension, radon exposure-associated effects on human health.