Simulating and predicting water levels in river systems is essential for flood warnings, hydraulic operations, and flood mitigations. In the engineering field, tools such as HEC-RAS, MIKE, and SWMM are used to build detailed physics-based hydrological and hydraulic computational models to simulate the entire watershed, thereby predicting the water stage at any point in the system. However, these physics-based models are computationally intensive, especially for large watersheds and for longer simulations. To overcome this problem, we train several deep learning (DL) models for use as surrogate models to rapidly predict the water stage. The downstream stage of the Miami River in South Florida is chosen as a case study for this paper. The dataset is from January 1, 2010, to December 31, 2020, downloaded from the DBHYDRO database of the South Florida Water Management District (SFWMD). Extensive experiments show that the performance of the DL models is comparable to that of the physics-based models, even during extreme precipitation conditions (i.e., tropical storms). Furthermore, we study the decline in prediction accuracy of the DL models with an increase in prediction lengths. In order to predict the water stage in the future, our DL models use measured variables of the river system from the recent past as well as covariates that can be reliably predicted in the near future. In summary, the deep learning models achieve comparable or better error rates with at least 1000x speedup in comparison to the physics-based models.