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In this work, we aim to accurately predict the number of hospitalizations during the COVID-19 pandemic by developing a spatiotemporal prediction model. We propose HOIST, an Ising dynamics-based deep learning model for spatiotemporal COVID-19 hospitalization prediction. By drawing the analogy between locations and lattice sites in statistical mechanics, we use the Ising dynamics to guide the model to extract and utilize spatial relationships across locations and model the complex influence of granular information from real-world clinical evidence. By leveraging rich linked databases, including insurance claims, census information, and hospital resource usage data across the U.S., we evaluate the HOIST model on the large-scale spatiotemporal COVID-19 hospitalization prediction task for 2299 counties in the U.S. In the 4-week hospitalization prediction task, HOIST achieves 368.7 mean absolute error, 0.6$${R}^{2}$$$R^2$and 0.89 concordance correlation coefficient score on average. Our detailed number needed to treat (NNT) and cost analysis suggest that future COVID-19 vaccination efforts may be most impactful in rural areas. This model may serve as a resource for future county and state-level vaccination efforts.