I live in Pittsboro as well, and it is a fairly small town with roots in agriculture and a large arts community. As far as restaurants go, the two big ones are The General Store and The Carolina Brewery, and I've heard Virlie's in downtown is good and S & T's Soda Shoppe, which is awesome.
One consistent event we have here in town is First Sunday, where street vendors line the sidewalks of downtown on the first Sunday of every month. (
Pittsboro Merchants Association)
From April through November we also have I think 3 farmers markets now in town, that have lots of really great produce and baked goods.
Here's a list the local Chatham Records newspaper put out with fun things to do around Chatham that might help you get a better idea of the things to do in this area:
20 fun things to do in Chatham (Chatham Journal)