David, on almost every trip since 1988, we've rented a gite rurale so we can cook some meals, buy some charcuterie and actually enjoy the bottles of leftovers the winemakers offer after opening them for tasting with us.
For cheese, the best epoisses in the region (still made with raw milk and , therefore, not imported into the u.s.) is the Gaugry fromagerie. A few years ago they moved from a little shop in the villages of Brochon (just north of Gevrey) to a modern facilities and shop on the main road in Brochon. (They make the cheese there, as they did in the old place; I took a tour years ago there,dressed like a surgeon.) They make a bunch of different cheeses with their milk and, also sell others' cheeses from the region and the rest of France. I know of no better place for that, and they will cryovac for travel.
There is also a marche in Nuits St. Georges on Friday....and a huge, permanent marche in Dijon that is amazing. For charcuterie and meats and poultry, both cooked and raw, there are some good establishments in Nuits on the main shopping mall, Grande Rue. Good bakeries, too for bread and other things. They have much more regular hours and you can bump into the winemakers in them. The place we love I can't find on the internet, but..that street can't be beat for your purposes, though veggies are best left to the marches.