Normally, the first to mid April would be the best, but nights have been chilly so around the 15th might be the best. I wouldn't wait until the end. Middleton Place is near Magnolia Plantation and I think (my opinion onlyLOL) that it's the better one. Since you are already in the area, try to see it too. I think you might could skip the tour of the houses as the grounds on both places are really outstanding.

Here is a link that might be useful: Middleton Place