Campground suggestions Shiloh, Vicksburg, Chattanooga

I would say in Chattanooga choice 1 would be Holiday Trav-L-Park #2 Chattanooga South KOA
Holiday Trav-L-Park is closer to downtown Chattanooga, and IMHO a nicer campground. The KOA is closer to the main Battlefield and Park Headquarters. If just visiting the Civil War sites is your main focus then these 2 are the best choices. If you want to stay a few days and have a more park like campground, then Cloudland Canyon or Chester Frost would also work, but your going to be much farther away

Edit: In Savannah doing what you are I would also stay at Fort McAllister State Park. Sherman’s march to the sea ended with the siege of Fort McAllister.