Well, there are members on this site who are members of private clubs; they might be so kind as to invite you to play their courses, however, I will not mention their names. However, near Raleigh I would recommend (public) NCSU Lonnie Poole, The Neuse and River Ridge in that order. Haven't played much in Durham. In Greensboro, either course at Bryan Park is pretty good. Oak Hollow in High Point is an older Pete Dye course, perhaps not what you had in mind but a fair place. As far as in Pinehurst, the priority would probably go #2, #4, Pine Needles, Tobacco Road and so forth.
Are there any designers or particular styles that might interest you that perhaps can't be seen elsewhere?
As much as I rip on Tobacco Road, that is a must see, I think.