Another vote for Dijon from me.
I rented bikes in Dijon and cycled to Beaune, had lunch, then stopped for wine tasting along the way back. Late September. A terrific day. It's an easy ride, some segments with traffic in town (in general drivers over here are much more accommodating and safer around cyclists than in the US). Lots of little roads thru the vineyards where the only traffic you'll see is the occasional tractor.
Copy-pasting something I posted to a similar question earlier this summer with some specifics. That was a longer trip, but might be helpful. I will add that I stayed at the Jacquemot in Dijon, and would not recommend it. Had a rooftop access, top floor room (requested a quiet room) and it had a terrible sewer gas issue that was quite unpleasant. Other parts of the hotel might be fine. I don't know. The bike rental outfit we used was close to this hotel. Good equipment, very nice people.
In Dijon, the tour of the Tour is very good. Operated by the tourism office. There are scheduled times each day and you should get a ticket ahead. Good meals here at Hotel de la Porte Guilliame (totally old school. Order snails.) Also L'escargot, which doesn't look like much but the kitchen knows what it is about (a swoon-worthy Tarte l'Epoisses) .
We had an outstanding tasting experience at Ch de la Tour (right next door to the Clos De Vougeot museum). We rented bikes and cycled from Dijon to Beaune and back, tasting our way north.
I prefer Dijon to Beaune as a town, although the Hotel Dieu is a world class site. Ma Cuisine is well known by Brits and Americans--it really is good and they had a fairly epic wine list. We also enjoyed Le P'tit Paradis.
Mercurey has a cave operation in the center of town now that is very well stocked and staffed. A good place to taste and buy bottles from small producers. In many places it's really hit or miss to find anyone who can serve shoppers at the wineries--the operations are mostly quite small and they are busy farming.
In Meursault, Domaine Javillier runs a cozy tasting space for their excellent wines.
Saint-Aubin also has a communal tasting room we visited.
Flavigny is a terrific stop. If you go that way, try to time it to have lunch at La Grange--cafeteria style, delicious food. And you sit at long tables with all the locals. It's a hoot. Very pretty village. I love Avallon too. Excellent Saturday market there. Had an outstanding dinner at Hotel de Moulin Ruats just outside town.