Vicksburg National Military Park, Mississippi
As a child my family visited the Vicksburg National Military Park just about every year. It is the preserved battlefield of the Battle of Vicksburg; the park overlooks the Mississippi River.
We once took a picnic and some pieces cardboard and slid down the grassy hills. As I grew older my scout troop visited the park regularly; we would walk the park which is either 7 or 16 miles, depending which turn you take.
I took my fiancé, who was from NC, there shortly after he proposed. We spent the walk planning our lives together. I remember it was June and quite warm, and we didn't have quite enough water with us. Fortunately, we came across a lemonade stand as we were leaving the park. That was a lovely day.
If you are traveling through the great state of Mississippi, I highly recommend visiting the Vicksburg National Military Park. If you are just driving through the state this is a great place to get out and stretch your legs. It is also rather easy to get to from the interstate. You can either walk or drive through the park, and it is a great place for a picnic.
If you walk take lots of water. There is a museum which is air conditioned. There are also monuments throughout the park to the various regiments that fought in the battle. The park is on the Mississippi River and there is an interesting exhibit of a Civil War ironclad. Here's the website: http://www.nps.gov/vick/index.htm