You asked for it, so here are my recommendations:
Downtown there are two decent places to try: Clyde Cooper's BBQ and Catering, and "The Pit Authentic Barbecue".
Cooper's is the real deal - typical eastern North Carolina chopped pork barbecue! They have lost a wee bit of greatness since Mr. Clyde passed away a few years ago, but they are still the best in the area. Their pork is moist and flavorful, but a bit chewy. It comes with great Cole slaw (finely chopped with LOTS of dressing), wonderful hushpuppies, and they even throw in a few home-fried pork skins! Their Brunswick stew is a bit too thin and their potato salad tastes like it is straight out of a can, but if you are looking for good "Eastern style" North Carolina barbecue - you will be at the right place!
"The Pit" is something a bit different, but good in its own right. Linen tableclothes and knapkins, with an extrnsive wine list (not to mention the "wine cellar" located behind a glass wall). Ed Mitchell - formerly of "Mitchell's BBQ" in Wilson, NC (before he went to prison for tax evasion) - now has a NICE place to peddle pork! The "Chopped Whole Hog" was a wee bit dry and chewy, but had really good taste. The flavor was slightly smoky with a good vinegar twang and a little heat (red peppers) - just like "Eastern Style" ought to be. Cole slaw was way too chunky without much dressing, puppies were okay, but their Mac&Cheese is really good and cheesy! They like their food a great deal as the cost reflects, but it's worth a gander if you have time and money.
In my rating system, I gave Cooper's a 4.0 and The Pit a 3.5 on a 1-5 scale with 5 being the best. There are other Q-joints in the area, but these are the two I'd recommend.
If you want more or will be outside of Raleigh just let me know as there are LOTS of other barbecue places around.
Good luck and I hope you enjoy!