Burgundy Villages Hotel, B&B Recommendations

I recommend that you stay in Beaune or Dijon( City). Beaune has a lot to offer. The countryside is vineyards and wine villages which you do not seem to be interested in. This is a wine center. Pretty area. You can take a train there from Paris or drive.
We stayed at Hotel Le Cep in Beaune which is an historic hotel in the center of town, lovely but pricey.
Also look at Vezelay, set on a hilltop.

I stayed in Avallon with a car and explored that part of Burgundy - Vezelay, Noyers, Auxerre, Fontenay Abbey, and much more. With a car I'd avoid the big cities like Beaune and Dijon - you'll waste time driving in and out of them in traffic.

I've stayed in Burgundy many times, both north, central and south. If you're not particularly interested in wine, the area that Chani suggests is a good choice. It's beautiful, and while wine is not a focus, there is plenty of that, particularly Chablis.

Check out the Carpe Diem Guesthouse in Massangis. The village is very small but several restaurants are in the vicinity ( We passed on the B&B dinner add-on, but other guests enjoyed it very much). I count it as perhaps the best B&B we have ever stayed in. Beautiful, huge room with sparkling new bathroom, gracious and helpful hosts, lovely grounds, parking, and driving access to many interesting sights. We visited many of the places Chani mentions, and also the renowned Romanesque cathedral at Autun We spent nearly a week in Burgundy and loved every minute, in large measure I suspect because of the Carpe Diem. Safe travels.

Thanks SO much, everyone, for excellent advice! I am in the process of booking a room at the Carpe Diem B&B, which fits our needs perfectly. Thank you for the recommendation, Denny.