Knowledge of the frequency of extreme sea levels informs construction of coastal defenses, flood insurance policies, and strategic coastal adaptation plans. In the midst of climate change, and particularly of intensifying and/or more frequent storms around the globe, accurate information about the frequency and magnitude of extreme storm surge becomes increasingly important. To date, such information is mostly available where tide gauges are installed. However, for comprehensive coastal zone management this information is equally important at ungauged sites, especially when coastal communities exist nearby. In this work, we use still water level measurements from tide gauges along the US Gulf Coast, and in conjunction with atmospheric reanalysis data (ERA5) we develop a Bayesian hierarchical model (BHM) to estimate extreme storm surge frequency. Our analysis demonstrates that the model yields extreme storm surge return levels with relatively small uncertainty compared to best-practice Maximum Likelihood analysis. The structure of our model allows us to provide spatial maps of extreme storm surge frequency information along the entire Gulf Coast, even at unmonitored coasts. These maps indicate that the BHM successfully captures the interconnectivity of extreme seas and clearly show meaningful clusters of storm surge hazard around the domain of interest. The results of this study will be of interest to decision makers, engineering design firms, and flood insurers, assisting them in adapting to imminent coastal flood risk.