Two suggestions that seem to be open are Bistro de l’Hotel and le Montrachet. Another one that someone in our party suggested (which I have not heard of) is La Ciboulette. Any thoughts?
Le Chambolle in Chambolle Musigny is one of our favorite restaurants in the Burgundy region and they are open Sunday evenings.
http://www.restaurant-lechambolle.com/index-uk.html
The Hostellerie de Levernois is open - both the casual bistro and the gourmet restaurant. Two solid options given the excellent wine list, beautiful grounds and solid cooking.
Bistro de l’Hotel was on our go to list for years but we dropped it after a couple so-so meals. Wine list is expensive. La Ciboulette is serviceable but nothing special.
Agree with John’s recommendations.
Our Sundays there now are lunch at either La Ferme de la Ruchotte or Lameloise. Couldn’t be two more different experiences but both very enjoyable. For dinner, we then eat lighter on market foods we picked up in Beaune the day before or in Chagny the day of.
I agree that the Hostellerie de Levernois options are very good, as is le Montrachet.
Another Sunday option is the Castel de Tres Girards in Morey. The cooking is excellent. The wine list is young, but I believe on Sundays offers all of the Morey wines (perhaps limited to villages and 1ers) at their purchase price ex-domaine (some shockingly low).
Lea Jardins des Ramparts; ate there twice my last visit.
Howard, you got me worried because we intend to dine at Aupres du Cloucher on the Sunday that we are in Burgundy in late June. We’ll phone in the right timezone to check that it is open.
Le Montrachet is good and I like Bistro de l’Hotel more than Paul (but the wine list is expensive).
Unfortunately one of my favourites, Millisime in Chambolle, is closed on the Sunday.
Andy, thanks for the Morey recommendation. We’re staying in MSD so may check it out.
Cheers, Howard
If it looks like it’s going to be decent weather, go out to Levernois. It’s a 10 minute taxi ride from the center of Beaune. It’s a special place, excellent wine list and equally great food. I’ve been there a few times in May, and we had our aperitifs out on the patio while we looked at the menu and took our first look at the wine list. It’s a very nice to start to the evening. Even in cold or rainy weather, they still seat you in the parlor for aperitifs, it’s just not as unique as the patio. This is for the main restaurant, I’ve never been to the bistro, but I’ve seen good reviews. Actually, I just checked their website, the main restaurant is closed Sunday dinners, but the bistro is open: → Bistrot du Bord de l'Eau · Restaurant Bistrot à Levernois
La Ciboulette is a much more casual choice, right in Beaune, very good food and a decent but much smaller wine list than Levernois.
Le Benaton is also open Sunday nights, it’s very good, and just 50 meters outside the walls of Beaune.
Hi Howard,
They are normally closed only on Tuesdays and Wednesdays. You can email them at contact@aupresduclocher.com for a reservation. I just did this last week.
I don’t think it is a Sunday issue. We are going in mid-July and they are apparently closing by then for their August break, as I understand it.
and epic cheese course!
Thanks everyone, valuable information on a few restaurants I hadn’t known about for my trip next spring.
If you can get in to La Ferme de la Ruchotte…and find it… 
Dad and I have eaten there twice, two of the 15 most memorable meals I’ve ever had in my life in terms of food quality.
Mike