I hear a lot of good things about Sugaw Creek and Hornet's Nest. From Charlotte, Rock Hill is maybe 30-45 minutes away, which means that Winthrop is only 30-45 minutes away.
Raleigh has some great courses with Cedar Hill and Buckhorn at Harris Lake. Chapel Hill is 30 minutes away with a good course.
If you're going by the west side of the state, check out Richmond Hill at Asheville and the course on campus at Mars Hill, about 20 minutes north of AVL. RH is a tightly wooded course with quite a few shots that play over a valley. MH is longer with a good variety of open and wooded, as well as long and technical. #7 is beast with the wind.
Further north is West Jefferson, about 30-45 minutes east from Boone. This course is challenging with a variety of shots that incorporate the natural elevation differences, woods and the lake. About another hour east from West Jefferson is Yadkinville. I haven't played the course(s?) at Yadkinville but I hear that they've got a good scene there.
And I can't forget to mention Hickory. Glenn C. Hilton park is a great course with a variety of shots that play through the woods, with elevation coming into play on several holes.
"Hit me with your wisdom, cow."