Here we present a new compact design of a vertical water distillation tower based on solar stills. The experimental setup consisted of a vertical tower with five water trays, supported by a metal duct and surrounded by a glass enclosure. The water yield and thermal, exergic, and economic features of the tower were investigated and analyzed. A new performance prediction hybrid model was also developed. A powerful artificial intelligence tool called the random vector functional link (RVFL) neural network was integrated with the Runge Kutta optimizer (RUN) to predict the water yield and temperature of the established tower. The model efficiency was compared to that of pure RVFL and an optimized RVFL model using a particle swarm optimizer (PSO). The drinkable water yield of the proposed design was 2.1 L/m2 (considering the tray area) and 5.3 L/m2 (considering the land use area); energy and exergy efficiencies were ∼31.7% and ∼3.3%, respectively. The cost of the produced drinkable water was approximately $0.013/L. The developed system provides considerable improvement compared with conventional designs of solar stills. The proposed RVFL–RUN model outperformed the pure RVFL and RVFL–PSO models for predicting system performance. The coefficients of determination between the experimental water productivity and water temperature and the predicted values, using the RVFL–RUN model, were 0.91 and 0.97, respectively.