There is a cafeteria downstairs in the MD11 sim building (we call the building AOTC) - open during lunch time for sure - not sure of the exact hours - decent food - short-order line, salads, sandwiches, pizza, etc.
The AOTC building is in a FedEx compound on the west side of Airways Blvd (west of the airport) - I'm not sure if hotel vans can pick up or drop off at the AOTC building inside the compound or not?
If you have wheels, you can go outside the compound to eat but not much of a choice immediately outside the compound near the airport except standard fast food.
10-15 minutes drive can get you to either Southaven (to the south) or southeast part of Memphis (to the north) where you might have more luck finding better restaurants/bars.
If you don't have wheels, it's gonna be tough - cafeteria and/or hotel bar/restaurant and/or walking (YIKES!!)
Good luck.