Concurring with most that Pinehurst, no 2, Mid Pines, Southern Pines, Pine Needles, and Dormie Club are the way to go!
Charleston gives you a great contemporary experience, but also a true Southern sense, the bad and recent good. BUT, I personally prefer Harbor Town and Hilton Head. I wouldn't spend that much time there, just play Harbor Town and drive down to Sea Island.
I also think the criteria would include Streamsong, which I imagine, would be great in mid March. As a reformed South Texan, mid March is about the comfort cutoff for that latitude.
Sounds like a great trip!