You're not going to have exciting and unique food choices for lunch along the way. There's the usual fast food choices. If you're not familiar, there are a couple of fast food chains that are not nationwide:
Bojangle's: started in Charlotte. It's a chicken and biscuit fast food place. Think of cajun seasoning... but not hot/spicy. Known for chicken filet biscuits. Side items of note: seasoned fries and "dirty rice."
Cook-out: This is a simple (and not fancy) fast food chain that is popping up everywhere in the Carolinas. The restaurant buildings are rather plain (far from tendy or plush). A few locations are drive through only. Think of this as a cheap Five Guys. If you look past the buildings and the generic foil burger wrappings, the food is actually quite good. The burgers are fresh meat (not frozen). The chopped BBQ is surprisingly good and gets rave reviews. The shakes are noteworthy. Note: They offer some combo meals called "trays" and are quite a bargain that include a drink. The trays are usually a burger and two sides. Sides can be anything from onion rings, hush puppies, chicken wrap to a corn dog (my wife has a lot of trouble thinking of a corn dog as a side). You may have moment of disappointment when you open up the styrofoam container and see small portions of the sides... but remember this is a "cheap" place... and you will be full after you eat it all. You can be a true southerner by changing your drink choice to a "Cheerwine" float. For those who don't know, "Cheerwine" is a Carolina born soft drink-- slightly like a cherry Coke.
So if you have to do fast food, those options offer a nice diversion from the usual.
You may want to give yourself plenty of time -- you never know about traffic. We always seem to run into a wreck or highway construction between Charlotte and Hilton Head. If you allow plenty of time and find yourself getting to Charlotte early-- I would suggest visiting the Billy Graham Library. It's about five minutes away from the airport. It's free. I've taken out of town clients there and they've found it extremely interesting. Very will done.