Integrated energy systems (IES) hold the promise of creating efficient, affordable, and reliable energy generation and delivery technologies. Specifically, nuclear-integrated hydrogen production using PEM electrolysis enhances nuclear plant flexibility and diversifies their product portfolio beyond electricity. However, the success of these applications requires a thorough understanding of their economic viability and the effects of safety and reliability issues on their economic performance. In this work, we develop a techno-economic analysis to determine the levelized cost of hydrogen (LCOH) produced from a 120 MW PEM electrolyzer co-located at a nuclear power plant. We examine the variation in net present value (NPV) for this system due to a range of hydrogen selling price values. We use sensitivity analysis to determine the impact of major cost categories, such as capital cost and system availability, on the LCOH. Finally, we compare LCOH ranges for PEM electrolysis integrated with various energy inputs (e.g. nuclear, solar PV, wind). Our results suggest a $6.5/kgH2 production selling price is the most attractive scenario, yielding the shortest investment payback period and highest NPV, or a $5/kgH2 production selling price with a slightly longer payback period. Our results indicate that nuclear-integrated hydrogen production can be the lowest cost clean hydrogen production pathway.