Public bathrooms, no. However there are many resorts along the beach. Just simply take one of the many beach entrances into a resort, act like you belong there, use the nearest bathroom, then GTFO. I do it a lot and have not had any issues.
Go to hiltonheadislandsc.gov/ourisland/beaches.cfm for info on all the public beaches and related amenities, but it says Folly Field Beach Park has restrooms along with metered parking & showers.
I did not see any at the areas I went.
I don't remember there being any public restrooms close to folly Beach but there are some areas that have some very nice restrooms.
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