Hotel or Airbnb for French Riviera?

I looked at La Grande Bastide in St. Paul De Vence but was nervous
about getting around by train since there isn't one there.

There is no train but a bus stop "Les Côtes" right in front of the hotel with bus lines 636 and 655 going to Cagnes sur Mer.

Anyway. From the moment you want to avoid crowded and urbanized places you will either have to have a car or take buses if there are any.

That is so good to know! We are okay with crowded places in general, like trains and for some day visits, but would just prefer to stay at a less crowded hotel if that makes sense? We will be renting a car our last day there to head over to Aix-En-Provence for a few days since it seems to have less public transportation.

If it helps you to find some places to stay, accessibles by bus check out the area's bus lines.

For Nice, Saint Paul de Vence areas click on "Alpes-Maritimes" (ZIP code starting with 06)

https://zou.maregionsud.fr/en/se-deplacer-en-bus/

For the Aix-en-Provence area click on “Bouches-du-Rhône” (Zip code starting with 13)

The train lines are here:

https://zou.maregionsud.fr/en/travel-by-train/

Staying in St. Paul de Vence is difficult without a car, as the bus connection isn't the greatest for the train station at Cagnes-sur-Mer. The village itself can get pretty trafficked during the day and the quiet gites and rentals are a bit outside of town. Instead, I would look at another town, like Beaulieu-sur-Mer, with a good train stop and a nice center.. Villefranche-sur-Mer can get overrun in the summer and the quieter locations up the hill add a tiring hill climb.. Antibes may appeal, but there is a larger walk to the train station from the old town. You can also chose quieter locations in the larger places. For example, in Nice, along Blvd Victor Hugo is much quieter than the Old Town or in the center of the pedestrian zone but a tram is readily available and the train station pretty close..

Nice is no more crowded at the end of August than any other place on the Riviera. It's just larger. For going along the coast, the train, with more seating available, is preferable to the bus.