I live near Beaune and I can't think of any memorable restaurants right in town. But there are lots of adequate places. I say adequate for Burgundy because they would be excellent in a lot of other places. Just walk around the center and you'll find plenty.

If you have wheels, just outside of Beaune there are several amazing places. In Chagny you have the top restaurant in all of Burgundy, Lameloise. Just to the north on the road to Pernand Vergelesses you have probably the top modern restaurant in the region in Charlemagne. And if you like great wine and art I'd recommend Château de Pommard just to the south of Beaune. They serve an excellent lunch. Reservations recommended at all these places, especially Lameloise.