I worked in Natchez for a while the last couple of years. The Magnolia Grill on the River is great food.
It is not part of a chain. Never had a bad meal. http://www.magnoliagrill.com/menu.html
Could be considered little pricey but well worth it. Don't forget to order the fried pickles. They are the best ones I've tasted.
The Eola Hotel on Pearl street has a great lunch buffet. If they are having fried chicken you are in luck. When I was there the wishbone was a cut from the chicken which is unusual (and I took full advantage of it) but I certainly complemented the Kitchen those days. Nice parking across the street. We would call to see what the menu was for the day. Usually good fresh vegetables.
Mammy's couple of miles south of Natchez on 61 is great for lunch depending on the day. If they haven't changed the menu I believe it was Black Beans on Monday, Pork Tenderloin on Thursday and the best chicken pot pie on Friday. The Hummingbird Cake is Great for dessert. Sorry I can't remember Tuesday or Wednesday.
Finally, BBQ http://www.pigoutinnbbq.com/.
This is good. Just looked up website and evidently I'm not the only one to think that it is good.
Have a great trip.