Bill,
I’ve visited most of the Civil War sites in the west, but not many in the eastern theater. You will be passing close to Shiloh which is a good park but if your wife is like mine there is a limit to how much you can see (she will put up with) at one time.
Sad to say, I have not been down Hwy 61 for a while. It should be a very nice ride but will get very busy at Baton Rouge. I would suggest you take the ferry across the river at St. Francisville then the New River Road (415) down to 190 and into Baton Rouge or to I-10.
Mark