Florence National Cemetery is a sober historic stop rather than a conventional attraction. It was established during the Civil War for Union soldiers who died at the nearby Florence Stockade, and it later became the burial place for veterans from later American wars. Rows of white markers make the history plain without much interpretation.
Visit it together with the Florence Stockade site if you want to understand the city's Civil War layer. The cemetery is quiet and formal, so the point is not sightseeing in the usual sense but context: Florence was not just a rail town, it was part of the war's prison-camp geography.