Personally I prefer Dijon to Beaune. There are sights in Beaune that are worth visiting but the center in Dijon is much nicer IMO. Rick used to take his tours to Dijon but I think he opted for the smaller city.
If you have cars, Semur en Auxios is more central and one of the prettiest villages in an area full of pretty villages (Beaune is not one of them). To me the best part of Burgundy are the medieval stone villages interspersed with rolling hills, small forests, farms, livestock and (surprisingly) sparse vineyards.
A week is plenty of time to explore some villages, sights in Dijon and Beaune, wineries and other sights. In fact, you could spend four days there then train or drive from Dijon to Colmar (I drove) and spend several days in Alsace. It's not far but a completely different feel. Between the two of them, you may overdose on charm.
There are three historical things you might love (depending on how much you like history): the Battle of Allesia museum (Julius Ceasar defeats the Gauls), Bibracte (Celtic museum and ancient ruins) and Guedelon (a castle, and open air museum, being built with 13th century tools and plans) a little further west.
Train stations will be at the south end (Dijon and Beaune) or at the north (Auxerre). When I went, I trained from Paris to Auxerre, rented a car and explored north to south, then over to Colmar, explored Alsace up to Strasbourg, then by train to Reims (for a night) en route to Paris. I think I spent ten days for the loop (but also added a night in Freiburg and Heidelberg, Germany, before leaving Strasbourg).