Over the years I’ve been to Shiloh several times and visited Corinth, Mississippi, as well. Corinth’s really developed as a Civil War site over the years, and next time I’ll spend more time there … including a visit to the site of the contraband camp established there during the war.
Like Fort Monroe, which has received attention recently for becoming a park that will, among other things, commemorate the even that led to the origin of the word “contraband” to described former slaves who had escaped to Union lines, the NPS has opened a park dedicated to exploring the process from slavery to freedom. Kevin Levin mentioned the park three years ago, so this post serves as something of an update to his comment.
There is no reason not to define “Civil War site” as something more than battlefields or places of military significance. A site like this, much like Birmingham’s Kelly Ingram Park, tells an important story in moving ways. I can’t wait to see it for myself.
Crossroads 
The Corinth Civil War Interpretive Center is a wonderful addition to Shiloh National Military Park. Corinth provides a unique intersection of topics that can help illustrate the Civil War in one, convenient geographical area. Within the small city there are opportunities to interpret a siege (April-June, 1862); a battle (October 3-4, 1862); a Confederate training depot; a Southern town under occupation (June, 1862-January, 1864); railroads and infrastructure; antebellum homes; hospitals; education (a girls college that was burned during the occupation) and, as you point out here, a unique chance to tell the story of the journey from slavery to freedom.
If you are going to Shiloh for the Sesquicentennial (April 6-8), schedule an extra day for Corinth.
I wrote all of this copy, and the Corinth Chamber of Commerce didn’t even pay me a dime:-).
I second everything that’s been said. The interpretive center at Corinth is great, and the whole town is a beautiful place to visit. The local museum at the railroad crossing is also worth a look.
–ML