Dijon or Beaune.
We prefer to take a train to Dijon, rent a car from there, but stay near Beaune.
Both are beautiful towns.
Last time we went south we found that it cost less, and is so much less trouble, to rent a car from Dijon than from Paris.
Dijon it is.
But before driving to Beaune, we like to spend a few hours in Dijon, have a nice lunch near the old market and then walk it off in the surrounding old town.
We prefer to stay near Beaune because there are many vineyard b&b's around there, whichwe love. You open your room window and it's vines as far as the eye can see. Not just any vine. It's Les Climats, the Beane winegrowing hills that are now a listed Unesco heritage.
As for your idea to stay in Avignon then do day trips to Arles and Marseille…
My suggestion is this:
If you have a car, why not go to the fabled villages in the Luberon hills, which are harder to get to, since you have a car? Of the hilltop medieval villages, my pick would be Goult, Saint Saturnin les Apt, Bonnieux. They are not museum-villages. They have bakeries, butchers, food shops, in short, the kind of good eateries and commerces that cater to locals. And when you stay in one of these 3 beautiful villages, you are actually in the middle of a cluster of beautiful villages. You never have to drive far to visit another charming spot.
Avignon and Arles are near each other. I prefer Arles as a base for its many Roman ruins and its greater concentration of good eateries, from Michelin temples to authentic Vietnamese. That's food- and archeology-obssed me.
But if you only have 3 days for the entire area, then you need to choose between Arles and the southwest side of Provence, and the Luberon hill villages. You can't do both unless you drive 20 hours a day. Even staying on only one side for 3 days is the kind of trip where you miss things more than you experience things. Can you allot more time to this area?