In Natchez, I can recommend Biscuits and Blues. They have great plate lunches, and the biscuits really are good. You'll also find good meals at the Eola Hotel and at Dunleith Mansion. I second the recommendation of King's Tavern, and the Pig Out Inn serves great barbecue and perhaps the best potato salad on planet Earth. Fat Mama's makes great tamales and yummy margaritas, and Pearl Street Pasta is a great local place, too. Under-the-Hill, you can try Magnolia Grill, but I tend to like eating in the old downtown better.

As for attractions in Natchez, touring the homes is always good. I love Longwood. (It's an unfinished mansion; begun before the Civil War started and remains unfinished to this day because its builder lost his fortune during the war. Very moving historical comment.) Rosalie is beautiful, also. If you have a chance to get out of Natchez a bit, I also recommend visiting Emerald Mound. It's an old Indian Mound off the Natchez Trace. It would make for a nice morning.

In Vicksburg, there are lots of little places up and down Washington Street where you can grab a bite. (Fun shopping on Washington Street, too. I highly recommend Attic Gallery. Art by Mississippi artists. Great prices.) You can also eat at some of the old homes. Cedar Grove serves wonderful meals, as does Anchuca. (Anchuca's breakfast is divine.) We also like Rusty's Riverfront Grill, and you MUST go to Walnut Hills. (Talk about fried chicken? Walnut Hills is the place you want to be. Portions are great, and the food is true Southern cooking.) You can also eat at any of the casinos located in the area, but we prefer the local places.

As for stuff to do, the military park is lovely and serene this time of year, and you can also tour the restored gunboat on the grounds. Many of the homes are open for tours as well, though I don't think they are quite as impressive as what can be found in Natchez. The Old Courthouse has some interesting things on display.

Hope this helps! Enjoy your trip!