I would recommend TWO areas to base yourselves out of - how many days are you talking about? You would need at least / min 2-3 days there to make it worth your time....since it's an AREA vs. just a city, the beauty of it is driving around all the quaint little hilltop villages and taking it slow. Provence is an area where you definitely want to have a car.
It takes four hours to drive from Geneva to Aix-en-Provence. If you base yourselves here, than you can easily access the "heart" of Provence - the Luberton hills, the medievel villages, the markets - you could actually hit Orange (famous Roman amphitheater) or Avignon on the way down. Avignon has the Palais des Papes and famous aqueduct....it's a big tourist destination so can get crowded and it's very lively/festive. Aix en Provence is the little Paris of the south.
The nice thing about Aix is that you can easily do a day trip to the coast...we love Cassis. IT's a seaside village that tourists don't seem to know about, but local French tourists love, and so do we. That's where we are headed....so you can get that cote d'azure feel but still be in Provence.
If you wanted to actually be in the HEART of Provence where they have the Mas de PRovence homes - the lavender colored shutters, lavender fields, sunflowers - basically, all that the impressionists painted - then APT might be a good place to base yourself out of and from there you take drives and meander around the most gorgeous villages like Rousillon, and Gordes - other even smaller villages we absolutely love are Bonnieux, Lacoste etc. Some of the most beautiful scenic drives are in this area - I remember one - windy and tiny roads but gorgeous is something like Tourettes sur Loup that Frommers recommended and I could find online if you chose to go to this area.
So the SECOND area I would recommend thought it's further from Geneva slightly b/c the way the roads are...would be the NICE / MONACO area. Now of course this isn't Provence Provence necessarily so you're getting more the FRENCH RIVIERA area....but it kind of gives you both b/c all you need to do is drive inland a little bit and you access PROVENCE and the cobblestone villages....like Grasse and Vence and St. Paul de Vence. These towns are bigger than the villages I mention above but you get the same feeling. It's always so fun to go to Monte Carlo and people and car watch and see the palace. Nice has some great museums - Matisse is my favorite there. WAlking along Nice waterfront is nice...but the beaches are pebbly and cold. From Nice it is fun to go into Italy for the day and have some pasta.