Provence base in September

Sounds like St. Remy to me! (Although I'm sure there are many other towns that fit the bill.) Check out the Hotel Sous les Figuiers website. Quiet, secluded, but close to town center.

Avignon is centrally located, with a variety of restaurants, hotels and B&Bs. Good train connections, including TGV.

I think Avignon is larger than it sounds like you are looking for. I agree with St. Remy. We were able to do many day trips from there. With 2 weeks, you may want to consider 2 bases of a week each. Additionally I would recommend renting an apartment or gite, as opposed to a hotel. It will likely cost less for a 2 bedroom place than 2 hotel rooms. For that length of time you might appreciate a kitchen, or at the very least a washer.

We spent a delightful week in the small town of Lourmarin a few years ago. It is on the flats so while you are there, little climbing. But, it is a short drive to a number of other towns that are typical Provençal villages on hills. We made daily trips, except when we wanted a do nothing day. Then we wandered the town, explored the shops, visited the grave of Albert Camus. It has a famous Friday market. There is a boulangie, several cafes and a few restaurants. We had an apartment and appreciated having a balcony at the end of the day for a nice rose and some chèvre.

Thank you all for your thoughtful information. Currently we are considering Gordes, Roussillon, and Goult. Any additional information would be greatly appreciated!

Arles has my vote, only because we stayed there for 5 nights - longest place we ever stayed in our 3, 1 month sojourns.