Dijon and Beaune restaurant recommendations
Being experienced Burgundy explorers you may know all of these, but just in case:
Definately hit the market (Les Halles) in Dijon on a Tuesday or Thursday morning for a great picnic!
I'd also recommend a cooking class from Alex Miles (an American ex-pat) if he is still doing them.
Outside of Dijon:
In Gevrey-Chambertin try Chez Guy. Great food and excellent wine selection (they always have my favorite Francois Lumpp).
In Beaune Caveau des Arches is still good, but moving away from great the last two times I've eaten there (Nov & Dec). I highly recommned L'Ptit Paradise or Ma Cuisine in Beaune. Also, just outside of Beaune in Buisson is La Buissoniere. It is very good too. There is always Le Charlemagne in Pernand-Vergelesses an entertaining Michelin one-star. Another recommendation in Beaune is less fancy, but one with awesome food - Le Gaspard (5-7 Place Monge).
I know you asked about dinner, but if you have time for a great wine lunch experience try one of these (but bring a driver or give yourself plenty of walking around time to sober up):
Pierre Bouree table' d'hote in Gevrey-Chambertin
Comte Senard in Aloxe-Corton (4, 6, or 8 wine lunch
A bit further south, but my favorite, Oliver LeFlaive (14 wine lunch - good night!
Lastly, for a different type of tasting try the best jam on earth at Frui-Rouge in Concoeur in the hills just above Nuits St. George: