At the Main Square in Beaune just outside the entrance and exit of the famous Hotel Dieu there is a market going on every Saturday. It is georgous! You find everything there - from fresh fruit to meat and cheese and if you walk down the Avenue de la Republique you will find clothes, jewellery and much more.
As well the Hotel Dieu - Hospice de Beaune is definitely worth a visit. I think it is the most beautiful former hospice of France. Nowadays it is a great museum - and when you see some of the doctors' instruments from then, I think you are happy as well to live in the 21st century :-)
Beaune is as well a place you get great wine as it is the capital of Burgundy wine. Go for a tasting - there is plenty of cellars who offer wine tastings.