ATLANTA — Drive through any state in the Deep South and you will find a monument or a museum dedicated to civil rights.

A visitor can peer into the motel room in Memphis where the Rev. Dr. Martin Luther King Jr. was staying when he was shot or stand near the lunch counter in Greensboro, N.C., where four young men began a sit-in that helped end segregation.

Other institutions are less dramatic, like the Tubman African American Museum in Macon, Ga., where Jim Crow-era toilet fixtures are on display alongside folk art.

But now, a second generation of bigger, bolder museums is about to emerge.

Atlanta; Jackson, Miss.; and Charleston, S.C., all have projects in the works. Coupled with the Smithsonian’s National Museum of African American History and Culture, which breaks ground in Washington this week, they represent nearly $750 million worth of plans....