1 $233: Charleston to Hilton Head on American Airlines - 1 stop (found 08/17/2016) 2  $413: New York City to Hilton Head on American Airlines - 1 stop (found 08/17/2016) 3  $458: Boston to Hilton Head on American Airlines - 1 stop (found 08/16/2016)  $438: Chicago to Hilton Head on American Airlines - 1 stop (found 08/15/2016)