I believe you’re thinking of Savannah International, which is about 30 miles southwest. It bills itself as Savannah/Hilton Head International, and it’s the biggest airport in the vicinity of Hilton Head, much more accessible from the broader US than HHH is, despite the fact that it’s in a different state.
I may argue this. There’s a lot of stuff here missing love. The majority of flights are between New York and Florida on the seaboard.. not me! Schenectady, Worchester, Asheville, Ithica, Rome, you name it! That’s my life, the lesser known flights of the sea board lol.
Speaking of Florida, a cool airport that is yet to get more attention is vero beach. The terminal is the size of a house. Served by two breeze planes at full capacity, the rest being a small ga airport. It’s one of those interesting airports in the world of aviation, but sadly, less known. Anyone reading this, check it out!