Nashville, then Memphis, then Vicksburg

Check out the Franklin (just south of Nashville) area for civil war sites especially the plantation with Confederate cemetery. Ft. Donelson is near Dover, Tennessee. Parkers Crossroads is also near Shiloh so you could stay at the CG at Parkers Crossroads and visit it along with the battle site of Parkers Crossroads (Nathan Bedford Forrest). There isn't much there (Crossroads)but interesting. If you go to Vicksburg, you must visit Natchez Mississippi to see the antebellum houses.

I also recommend visiting Andrew Jackson's Hermitage while in the Nashville area.