If you can't get on a private club, and you want to confine your travels to the Raleigh/Durham area, I would say Duke or Heritage would be your best bet. While choices like Tot Hill, Tobacco Road, Keith Hills etc., may be worth playing, they will be a bit of a hike. Even The Preserve is a bit of a drive, and not the easiest drive to make. If you want to play a better DL III course, play Anderson Creek (about an hour from RDU).
While Duke's conditioning may be an issue, it is a much better layout than Finley. I've played both more than a dozen times, and although Finley always seems to be in great shape, I find
it rather boring.