I second the mention of Cedar Hill Cemetery. Besides an extensive area set aside for Confederate graves, a different section dedicated to the Catholic nuns of the city is very moving. There is a lovely statue of the Virgin Mary, and a look at the nuns' simple gravestones shows that many were young convent women -- 18, 19, 20 years old -- who died in the yellow fever epidemic in the late 1800s (1870s? 80s?) as they served as nurses and became ill as well. The Sisters of Mercy convent building still stands as part of the Southern Cultural Heritage complex. The sisters first arrived in Vicksburg in 1862, if memory serves, and were an important part of education and nursing in the city into the 1990s.
Also visit the floodwall to see the murals. Go through the open section to see the back of the wall, where the heights of the most historic floods have been marked. It's amazing to see how high the river got!!
If it survived the covid shutdowns, Walnut Hills restaurant is a great place for a meal. And take a drive up Washington Street along the original Highway 61 to view what remains of Margaret's Grocery. As you drive up that part old 61 you'll get a different view of the Vicksburg National Cemetery on your right.
Such a wonderful little city! Enjoy your visit!