Wine taste at the Caves des Cordeliers in the middle of Beaune.
There is also a little wine tour that you can buy tickets and depart from at the Tourist Info in the center of Beaune.
If I can suggest a hotel, Hotel des Remparts. It is inside the old city walls... it's actually attached to them.
There is a Hertz Car rental at the train station and one fairly near (a few blocks) the hotel.
Ask the friendly staff about parking... I think it is on the street and it was free.
When you are driving around you will want to go to see castle La Rochepot.
It is in Rick's book. There is a rich history surrounding the burgundy area and this restored castle is an amazing site.
Stop into a winery at the village of La Rochepot (a little further down the road)
One thing on wine tasting, in France I have found it best to announce when you walk in that you are interested in BUYING wine and you would like to taste what they offer. Tasting is not the same there as it is in US