This statue of Ulysses S. Grant is located at the spot where his headquarters were during the Siege of Vicksburg from May through July 4, 1863. This location is the crest of a small knoll.
In downtown Vicksburg still stands the old courthouse. It’s a museum now filled with many artifacts from the war and that time period. You can see from these linked old photographs the structure had not changed. Notice the cysteines around the building. when you go to the museum be sure to talk to the curator who is well versed in the history of the siege and Vickburg and the civil war. 
Note in the picture below the Union soldiers carved their initials in the stone floor around the building after they took the city on July 4. This one is from a fella from the 45th Illinois Volunteers.
One of my favorite places to visit at the battlefield is the Cairo Ironclad. They pulled the remains of this ship out of the river in the 1960’s and have partially rebuilt her under these large tents. She was designed and built in Carondelet Missouri outside of St. Louis by Robert Eads, who later went on to build the famous Eads Bridge across the Mississippi River in St. Louis.
New Heitz 