From coastal South Carolina, we have -
grits - the good kind, stone ground!
cornmeal - same as above
Carolina Gold Rice - was the rice grown on plantations here, and is seeing a great revival by some artisan growers.
Shrimp/crabs - If I could pack it and take it w/me; otherwise, I'd make a shrimp or crab dip to take with me.
Carolina mustard BBQ sauce
Gosh - I'd better stop!