6 days in Nice, and looking for 3 days in Provence region for daytrips

If I planned to rent a car and had just three days, my focus would be on the smaller places, like Roussillon, that are difficult to access via public transportation. It's pretty easy to get to Marseille, Aix, Avignon and Arles by train; they can be part of your next trip to southern France.

I've never had a rental car in Europe, much less in southern France, so I can't provide specific guidance on getting around that way. However, it may be helpful to know that L'Isle-sur-la-Sorgue has significant markets twice a week that are fun to see but probably come with parking challenges. The market stalls also make it somewhat difficult to appreciate the beauty of the town, so if you have no interest in seeing a Provencal market, you would want to avoid L'Isle on Thursday and Sunday. The Sunday market is the larger of the two.

Maybe you're thinking, "Who doesn't love markets?" In that case, this website has a list of the markets in Provence listed by day of week: https://curiousprovence.com/a-list-of-market-days-in-provence/. The list was compiled in 2020, so it is imperative to verify the information by Googling something like market L'Isle-sur-la-Sorgue or weekly market Cavaillon.

I did not have a car in Nice, and here is where I went:

1. Cannes -- had lunch at a beach club, walked around
2. Antibes, same day, but we were exhausted, stared at the water, and left.
3. Saint Jean Cap Ferrat and Beaulieu sur Mer -- the Villa Ephrussi was AMAZING and not to be missed. Villa Kerylos not as amazing, but still cool.
4. Monte Carlo -- huge waste of time, wish I had done one of the ones I missed instead; Menton - very cute, but not as un-touristy as people said. The hike to the cemetery was intense; Ventimiglia -- we just walked around near the market and train station a bit, just to say we were in three countries in one day.
5. Villefrance-sur-mer -- we ended up spending the whole day here. We just vibed with it.
6. Don't forget to explore Nice itself! We missed: Eze (really feel bad about this one, but somehow we left it for a Sunday, and the logistics on Sunday with Eze without a car are not good); Aix-en-provence -- tricky to get to without a car; Saint Tropez; Saint Paul de Vence

Re: Provence, we stayed in Avignon, but only walked around Avignon at night. For day trips, we did Roman history -- a full day in Arles on our own, and then a day with a tour guide who had a car in and around Nimes. We saw Nimes itself, Uzes, and the Pont du Gard. This would not have been possible without a car.

Imo the first thing you should look into is the cost of renting a full-sized van. It might be cheaper to get 2 small cars.

2nd, is parking. We always rent small cars; but, even so, there have been times when maneuvering into and out of parking places has been challenging, (to say the least!)
Finally, on your town choices, the Cote d’Azur abounds with beautiful, interesting towns. I have been to Aix twice and didn’t warm up to it. The main attraction in Avignon is the papal palace, which is mostly empty inside. Iif you do go there, you should add the Pont du Gard to your excursion. Roussillon is a great choice. Eze and St. Paul de Vence are close to Nice and are other good options. If you are willing to go as far as Marseille, you might consider a calanques excursion, as well as a Camargue visit.
If you google town names, you will pretty quickly come to headings like, “What to do in . . .” Helps with choices.

If you are heading to western Provence, but don't want to go too far north, then can pick a base like Arles, St. Remy or Aix-en-Provence. It really depends on what you want to do? If you want to see coastal Provence, then consider Cassis or Bandol/ or Sanary-sur-Mer (note you will be at a busy time). Or for something in between, the area near Hyeres has access to the Porquerolles islands, inland to some nice villages, and access to the St. Tropez peninsula. It will be crowded though, in high season.

You can pick up your car/van at the Airport. Take the tram in to Terminal 2 and the car rental center is in the middle of the parking area. You can also pick one up at the train station, but the choice is less.

Jamsales,
I recommend Bandol for a place to base yourself in Provence. It is on the coast, has a small sandy beach, a harbor for private and small fishing boats, a promenade to stroll along the waterfront with nice restaurants and cafes. That is also where the farmer's market is (on Tuesdays, I believe). There are numerous wineries for tastings nearby, and a larger beach on the way to La Ciotat. It is a short drive to Marseille to see Le Vieux Port, Chateau d'If and Notre Dame de la Garde.

Aix, Arles and Avignon are not coastal towns, but are not too far inland. We like Arles and Aix. Avignon doesn't enchant or impress us, after we have seen the bridge and the (mostly empty) unimpressive Palais des Papes. If you do go inland a bit, Arles has some really nice Roman ruins (an impressive Colisseum, for instance) and a charming old center.
Be sure to research your travel drive times so that your return to NIce for your flight home isn't compromised. I take it you are planning to go back to Nice the day before your flight home.

Acraven is right about having a larger car in French towns and cities. Streets are narrow in the old quarters, especially. We have had rentals in many parts of France (even Marseille) and sometimes it was tight just driving, let alone parking. However, when you check lodgings at, say, Booking.com, put in parking as one of your parameters. There will be some places with on-sight parking. It takes some research. We at one time did have a sort of minivan, which we drove to Albi, Carcassone, Cahors, Sarlat and Nimes, from a stay in Marseille, and it wasn't fun for my hubby who drove. (We needed it for a family member with compromised health and mobility.)
Perhaps two smaller cars would be better. (We have had 3 adults and two kids, plus their carry-ons and backpacks fit into a mid-sized car, but their longest drive was no more than four hours. Doable, but not ideal.) We have also taken five adults in a mid-sized car for a drive from just south of Barcelona into France (for Carcassone by way of Andorra), but we didn't have all our luggage with us...just enough for two overnights. I am sure you will find a solution for all of you.
Bon voyage, bonne chance, et amusez-vous Bien!

Clearly there are half a dozen nice towns very conveniently located near Nice along the train line from Antibes to Mention. You can even slip into Italy. You can get way over to Avignon and its travel cluster (Arles, Nimes, etc) but it was 3 hours each way - maybe faster now that they have a TGV line. The classic Provence towns are all car destinations - Gordes, Roussilon, Lourmarin, Curcumin, Le Costa, Les Beaux, etc.

Responding to some other comments :

Recommended :

Avignon has the best restaurants in the area, city walls, the pope's palace, and I have used it as a base several times. They also have many festivals.

Antibes is fun and picturesque

Aix-e-p, has good art museums, and a vibrant student climate.

St Remy is a nice little town and has some significant Roman ruins just outside town.

Les Baux is impressive from a distance, and they have an Atelier d Lumber show which is great.

Nimes is nice though and has Roman ruins and a wonderful park and some good restaurants.

Bealieu Sur Mer and Villefranche sur Mer are nice albeit a little quiet.

Not Strongly Recommended

I have been to Arles 5 times and never really liked it.

Eze is not worth the effort in my view. Just a tourist stop up in the hills.

Nor Gordes or Roussilon or Lourmarin. They are just touristy facades in my view.

Orange has the big Roman theatre, but otherwise pretty small and not impressive.

Cannes and Monaco are ok but overly glitzy.

Menton - poor man's Nice. It's ok, and nice harbor with wall. a little low end

We much preferred Arles to Avignon.

After staying on the coast near Nice, we are taking a train to Aix and picking up our car there. We are staying just outside of Gordes and will have the car to explore that area of Provence for 3 days. We are headed on to Beaune after that so we will keep our car.
We always like to leave our departure city till the end of our trip. Can you flip your trip and do the Provence leg first and then return to Nice for the rest of your trip, and already be there for your flight home?