The places I've yet to visit in that state is Hattiesburg which has a family connection, Biloxi, and of course Jackson. A few years ago I had the opportunity to pay a visit to Jackson, however, time constraints nixed that opportunity!
C-Span speaks with Mississippi's Museum Division director of collections Cindy Garner who discusses the many items connected with that state's role in the Civil Rights Movement. So if there is going to be a Civil Rights Museum in Jackson, paying the capital city of Mississippi would be a worthwhile trip.