The Café de la Paix occupies a corner of the central place Carnot and is the town's quintessential all-day café — croissants and coffee at 8am, salads at noon, pastis and a game of pétanque from 4pm. The outdoor terrace faces the market square and is the best place in town for watching Beaune go about its business.
It is not a wine bar in any serious sense, but it serves a decent kir royale and a glass of local wine, and it is reliably open when everything else is closed. The kind of café that anchors any French town worth anchoring.