Hydrogen (H2) has the potential to become a clean fuel alternative to replace hydrocarbons in a low-carbon economy with H2 storage representing a key component of the emerging H2 value chain. However, the use of H2 for bulk power management and other industrial applications will require significant upscaling of geological storage. While geological H2 storage can take place in both porous media and salt caverns within salt formations, salt caverns are considered the best option for underground H2 storage for their large storage capacity, their sealing integrity, and their flexible operation with large injection and withdrawal rates. This study collects a comprehensive database of 569 salt domes located in the onshore and the offshore regions of the Gulf of Mexico Basin in the United States. This work filters the database by selecting onshore domes with no pre-existing caverns and a suitable depth range for salt cavern construction. As a result, we select and analyze 98 onshore salt domes suitable for H2 storage in the states of Texas, Louisiana, and Mississippi. We perform H2 storage capacity calculations for three scenarios: low, base, and high cases. For the base scenario, we estimate that these salt domes can accommodate a total of 2550 caverns, with a total working gas potential of 130 Gsm3, equivalent to a total energy stored potential of 368 TWh. According to our base scenario, a 10 % replacement of the natural gas consumption in the United States, could require a H2 storage capacity of 28 Gsm3. This number implies the construction or repurposing of more than 556 salt caverns with a geometric volume of 0.75 Mm3 per cavern. This study is the first of its kind, providing a breakdown of H2 storage potential by state, county, and individual salt dome in the states of Texas, Louisiana, and Mississippi. The findings from this study provide valuable information for assessing the H2 storage potential of salt domes in the United States, useful to assist in the definition of strategies to develop future H2 infrastructure. Finally, we provide the readers with an interactive map that displays the results of this study.