Nuclear hybrid energy systems (NHES) have the potential to provide dependable and emission-free electricity to the grid while also increasing the flexibility and reliability of the electrical grid. Molten salt reactor (MSR) technology can provide consistent, carbon-free electricity while also increasing efficiency, security, and sustainability and reducing nuclear waste. This study investigates the integration of Molten Salt Reactors (MSR) and conventional Pressurized Water Reactors (PWR) with desalination technologies: Direct Contact Membrane Distillation (DCMD), Multi-Stage Flash Distillation (MSFD), and Reverse Osmosis (RO). Dynamic first-principles models were developed and tested using real grid data from the New York Independent System Operator. The results demonstrate that nuclear power is capable of flexibly responding to changing grid demand while simultaneously producing clean water, particularly during periods of low electricity demand. The MSR-RO system was found to be the most efficient in electricity generation and water production, and all hybrid systems reduced CO2 emissions by 356,000 to 682,000 tons annually. Economic analysis reveals that nuclear desalination technologies are cost-competitive with conventional systems, especially when paired with RO. These findings confirm the technical feasibility and environmental benefits of nuclear hybrid systems for sustainable electricity and water production.