Brunswick, GA is reputed to be a hurricane haven and many east coast
boats opt to spend hurricane season there. It's not far up the coast from J'ville. 1.5 hours by car, more or less.
Whether or not it is really a hurricane haven, I could not say. It's quite a popular marina. The marina is set back from the ocean somewhat, up a creek, and seems like a stout and sturdy setup. Massive concrete piles, concrete docks, etc.
Regardless, it's an option to consider for east coast
boaters. You'd need to make your reservation early, as the place fills up quick.
It is accessible by ICW
and also has a wide dredged ship channel heading out to the ocean.
It's about a 12 hour sail from J'ville to Brunswick.