Mississippi is starting to get decent places to eat, especially in some of the suburbs of Jackson. On the edge of Jackson is Aplos, which promotes itself as Mediterranean food.
They offer Greek and Italian specialities and the food is quite good.
An interesting choice is the Gyro Pizza. Made with Gyro meat (Beef/Lamb), it comes with a side of Tzatziki sauce, you put it on the pizza and eat. Not exactly like a real Gyro, but it’s taste is quite close.