I'll second the Duke / UNC tours. Walking in downtown Raleigh is nice, too.

There are several malls in the area. Crabtree Valley mall is on the north side of Raleigh and has some interesting shops. There is another sizeable mall in Cary (the name eludes me). If you are into outlet shopping, nearby Smithfield, NC has a huge complex right off of I-95 (probably a good 45 minute drive away, though). Durham has a pretty interesting science museum, too, right outside of Duke.