Last year, we flew AirTran (out of Midway) into Atlanta, had a couple hour lay over and then flew from Atlanta to Savannah. It's a quick drive from Savannah to Hilton Head.
I have not been able to find a direct flight from Chicago to Savannah that didn't cost me an arm & a leg in airfare. I'll be anxiously awaiting other replies as we're off to Hilton Head in March. We've done the drive several years, but now that we've flown some, it's hard to go back to a 16 hour drive.
Have a great trip!