In the domain of RIS-based indoor localization, our work introduces two distinct approaches to address real-world challenges. The first method is based on deep learning, employing a Long Short-Term Memory (LSTM) network. The second, a novel LSTM-PSO hybrid, strategically takes advantage of deep learning and optimization techniques. Our simulations encompass practical scenarios, including variations in RIS placement and the intricate dynamics of multipath effects, all in Non-Line-of-Sight conditions. Our methods can achieve very high reliability, obtaining centimeter-level accuracy for the 98th percentile (worst case) in a different set of conditions, including the presence of the multipath effect. Furthermore, our hybrid approach showcases remarkable resolution, achieving sub-millimeter-level accuracy in numerous scenarios.