The Travelin Man
Hilton Head may well be the antithesis of "roadfood." Any destination for rich, white, golfers is not likely to have the indigenous shacks and joints necessary for true roadfood. You are way more likely to find more country club-like food — pretentious, overpriced, etc.
On the other hand, Hilton Head is not too far from Savannah, GA; Beaufort, SC; and, one of my favorite eating cities in the South, Charleston, SC. For me, if I were that close to Charleston, I would have a hard time resisting a trip there. But, you can find good options in Beaufort and Savannah. If you search on those terms, a number of threads will pop up.