For me I'd head straight to Avignon and stay at the R&C property Hôtel Le Prieuré. Have an nice gourmet meal and the next morning walk around the Prieuré (priory) and then into Avignon itself.

As for the amphitheater in Nimes, for me it wasn't worth the time. Nor Orange. I'd spend a night in central Annecy having a nice mountain meal there, relax and then tour around the lake in the morning. You can also take a cable car up the mountain for some spectacular views and fresh air.

Lastly why not visit Geneva for a few hours? There are some interesting museums. One of my favorites in the Red Cross museum.