Bruce, I used to live in Chapel Hill so I can give you a few poiinters here.
Neuse is pretty good. I enjoyed it a lot.
Challenege in Graham is a blast. I played it often and it is a real good day. Lots of interesting holes.
I never played the others you mention, but would offer this up to you. You do not have the University of North Carolina Finley Course or the Duke University Course. They are both fantastic courses and worthy to play. UNC was re-done by Tom Fazio and Duke is a RTJ course, with Rees Jones refresh. I can't tell you how much you will enjoy these 2 courses.
Bear in mind that a guy named TarHeel is recommending the Duke course! But that's only IF you play UNC as well.
Finally, if you could get on to Hope Valley Country Club (it's private), it's also a must do. It's an old world Donald Ross club. Awesome greens and a worhty club.
I'm jealous! Moved to Michigan from Chapel Hill in 2002 and miss it every day. Especially in April time, when the pine is so fresh and the flowers looking so lovely. Good luck.