I was there for 1 night last June. I drove from Chamonix, challenging when I got to Beaujolais since I then chose a scenic route (roads are narrow, no shoulders, poor signage, not well-maintained). GPS is essential! It is a very scenic area. I arrived on Friday evening, pretty town with some ancient buildings. I stayed at the Hotel de Bourgogne and loved everything about it - staff, location, comfort, lovely old furnishings (and modern bathroom- really the only "modern" part). The Abbey was interesting. I climbed the Tower, the views were nice but the bars on the windows spoiled it somewhat.
On the way to my next destination, I stopped at the chateau in Cormatin (a short drive from Cluny). The inside is only by guided tour (there are a few in English - check the times), the building and grounds are beautiful too, and storks nesting on the roof.