Thank you for all th advice and input!
I took some of your recommendations and revised the plans as follows:
Fly in to Nice - 9/9
Nice 9/9-9/12 - Radisson Blu/Hyatt
Cannes 9/12-9/15 - Hyatt
Avignon 9/15-9/18 - B&B in the city
Lyon 9/18 - Hotel near train station
Fly out of Lyon 9/19
We're using Avignon as a "base" for some small towns. We might rent a car, or we might use the train system to go from place to place. Right now we have an all day wine tour planned one day, one day for exploring the city itself, and one day open which we might use to go to Marseille just for the day.