I will be picking up a car in Nice (where do you suggest?). I will be coming from Cinque Terre by train. I want to drive from Nice to Avignon and back seeing some of Provence and the seacoast. I will have a week to see this part of France. What do you suggest? What towns should I spend the night in? I like small villages. I need your help.

You can easily drive from Nice to Avignon via the autoroute in a few hours, which would be my advice for the route west. Since you like small villages, you could stay near Gordes at La Ferme de la Huppe, a pleasant inn/restaurant (great food!) and explore the Luberon villages from there.
In four days you could range over to St-Rémy and Arles, probably the Pont du Gard.

On the way back to Nice you could follow the coast roads, which are very scenic but also slow. So it would be wise to spend the night somewhere along the way, and the hillside village of Bormes-les-Mimosas would be ideal. It's only about a 10-minute drive from the village down to the beaches at Le Lavandou.

We took the train from Cinque Terre to Nice and picked up the car at the train station. This was very easy to do - easy to drive out of Nice - we drove to St. Remy and stayed two nights - saw Arles, Pont du Gard, etc., then spent a night in Vaison. From there we drove to Lourmarin for three nights, seeing all the Luberon villages. We then flew home from Marseille. The only thing we didn't have time for was the coast which we are doing this next trip.

Pick up the car at the train station and then pick up The Route of Napoleon; perfect if you enjoy incredible scenery, spectacular roadside geology, and small villages. Send my best regards to Castellane!! If at all possible, hike to the top of the rock (you will know which one) and visit the stone chapel on top (dates back to 1703); amazing views from the top. Very touching testimonies left over from families of soldiers from WWI and WWII. Definitely worth the hike.

Forgot to post a website rec: http://www.route-napoleon.com/gb/index.html