We will be in Avignon mid October for five days. Will have a car and plan to stay in Avignon and take day trips to other cities in Provence and back to Avignon for the night. Is this a good plan, or would it be a better use of time to sleep in several other cities?
I would pick one other city to stay in as well. Probably Arles. Opens up a different area of Provence to explore and is a cool city on it's own. Arles is a little gritty compared to a more sophisticated Avignon but in a good way. We stayed at the Hotel Calendal with a direct view of the Roman Arena and enjoyed it very much. If you go make sure you try for the Saturday market. We also took day trips to AIX and Cassis for the boatride to the Calanques.
I will also be in Provence in October! I would either stay in the same place for the entire time, or limit it to two places at the most. If Avignon is a definite choice (I liked staying in Arles) I would make the second location be a village in the Luberon. That way you get a taste of a village and a city, plus you would minimize driving. One thing that should influence location would be where you are planning to go. If you want to explore the Camargue, a base in Arles makes sense.
Have fun!