I did it with a car and no tour. I visited Burgundy first, then drove from Beaune to Colmar. I was also there in mid-May. Early may was too early for Burgundy (at least in 2017). It was still cold, the vines were barely starting, most towns were empty and restaurants were noticeably closed. By mid-May, the towns in Alsace were much more vibrant (not quite packed) and everything seemed to be open.
Based on advice from fellow posters here, I limited the number of towns I visited. After Colmar I visited Eguisheim, Kaysersburg, Riquewihr and Ribeauville. Really each town is as beautiful as the last. Pick some that seem interesting to you and go with those, you can't really go wrong.
I also visited Chateau du Haut-Koenigsbourg, a very good castle. I didn't visit Monkey Mountain because I've seen Barbary apes at Gibraltar.
I ended in Strasbourg before training back to Paris (with a one day/night stop in Reims).
I had more days in Alsace than I needed so I also spent a day/night each in Freiburg and Heidelberg.
I had some wine but it wasn't the focus of my trip. I get more enjoyment from seeing the architecture and countryside than wine. My Airbnb host in Strasbourg gave me a really nice bottle of Gewurztraminer (the best of Alsatian wines IMO).