Burgundy is perhaps one of the best-served regions of France in terms of accommodations. The vast range has everything from simple gîtes d'étape (bed-and-breakfasts) to four-star châteaux.
Especially in summer, Burgundy is often overrun with tourists, so finding accommodations can be a problem. It's wise to make advance reservations, especially in the wine country (from Dijon to Beaune).