Last week I visited the Durham Wildlife Club's Tuesday Night Pistol Shoot. It starts between 6 and 630pm every Tuesday and seems to be mostly IDPA-style shooting. It was the first time I had done anything like that and I really enjoyed it. The group of guys were real nice and I learned a lot, made a few mistakes, but thoroughly enjoyed myself.
Here is a link for more information: http://www.dcwc.net/Tuesday%20evenings.html
Its not far from RDU.