Pittsburgh and Raleigh are about 330 miles apart by road. Split the difference and you arrive near Richmond, the city closest to the halfway point between them. That puts roughly 5 hr 6 min of driving on the Pittsburgh side and 3 hr 28 min on the Raleigh side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Richmond suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Richmond doesn't have what you're after, Washington and Charlotte are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Pittsburgh and Raleigh.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.