Provence for 10 days

You want a car to explore the country sights in Provence. But with a car, you want to avoid home basing in the center of these cities: Avignon, Nimes, Arles, and Aix en Provence. Reason is parking and traffic difficulties.
You can home base on the outskirts of those cities, just make sure your lodging has easy access from the main roads and secure overnight parking.
An alternative is to home base in country locations, use the car to see the country sights; and then on the days you want to explore any of those cities, drive the car to the nearest train station, park the car at the station for the day, take the train to those cities (good rail service to those cities), explore these urban locations on foot, return to the station parking lot at the end of the day, and drive back to the lodging.
For the country sights of Provence, a car is the best way to explore such destinations as Pont du Gard, Les Baux, St. Remy, etc.

"Playing at the beach for a few days" sounds more like a Riviera than a Provence thing. Most people reporting in here who want to spend that kind of time at the beach don't stay in Provence, they locate further east, towards the Riviera. Maybe that is where you should locate your second home base.

For a day with beautiful scenery and water play, though not a beach, look at a calanques visit. Cassis is one town close to the calanques, but there are others. Actually, I think there is a beach in the town. There certainly are some in nearby towns. Since the calanques region is close to Marseille, it might be a good place for getting over jet lag.

Instead of a beach day (or in addition to one), you can drive to the Pont du Gard and take a rafting trip down the river under the acqueduct, then come back and walk along it. There is a beach area there by the river (rocky/pebbly, as I recall). There are several companies that do the rafting trip - you can arrange to meet them at the starting point and they will take you back to that point after the rafting is done.

Zoe, if I'm not mistaken it's kayaking and canoeing that would be available near Pont du Gard, not rafting per se. I don't believe the water moves fast enough for rafting. Feel free to correct me, but as I recall that is the case.

Absolutely the Pont du Gard! The aqueduct itself is amazing to see and learn about, there is a great museum for kids and adults with a food court and the locals see it as a place to hang out, swim and sunbathe. Take towels and bathing suits and pack a lunch. There are canoe rentals but it's not the way most people enjoy the river. They hang out like a day at the beach.

Take a GPS with you that you are familiar with. We drove some one lane country roads that were great and never got lost. Sometimes I would turn off the toll road option to make sure we took the longer scenic route.

Thanks everyone for the recommendations. I'll start looking into all the ideas!

Cassis does have a beach. It is right off the downtown area. It is more pebbly than sandy though. If you want sandy beaches, try Bandol which is east of Cassis. I've been to both towns. Cassis is more charming as a town but Bandol has the better beaches. Make sure you know about parking arrangements before heading there. July is high season and everyone wants to go to the beach! Bon voyage!

See also http://www.ot-cassis.com/en/le-massif-et-les-calanques.html for the Calenques. On their pop-up map, the pink number 2 is for a bare-bones youth hostel (no showers, bring food to cook) in a great location, only accessible by car, then you can hike downhill to the water.

My favorite place to stay in Provence is St. Remy... a beautiful town with great shopping, restaurants and a fabulous market. Centrally located to lots of the towns you will want to visit and a beautiful approach as you drive into the town with the trees on both sides overhanging the road. An early morning hike to the hospital where VanGogh spent some years is a fun thing to do. You could take a drive (a few hours) to the Carmague where the flamingos and wild horses are as well as a beautiful little beach town. While the 'wild horses' are not running all over as I expected (they are fenced in certain areas) on one particular trip there were thousands of beautiful flamingos in a lagoon area right by the ocean. It was spectacular, and quite a different terrain.