Provence

More than enough... you will run out of time before you run out of interesting, wonderful things to do and places to visit. But... I love Provence and could never be bored with it...
What do you like to do when you travel?

Yes, absolutely. Would you have an even better trip if you spent some of your time differently? That I do not know.

Thanks for your quick response. Originally our thought was 1 week in Barcelona and then one week in Provence. Any thoughts about this? Also, what about one week in Alsace, France and one week in Provence? Or, as you have both said, 2 weeks in Provence with a lot to do there. Would you suggest a day trip to Nice, or is that too far? Appreciate all of your comments.

If you want two different experiences, then I would say a week in Barcelona and a week in Provence... actually I would do just 4 days in Barcelona and the rest in Provence. I like Nice, but there are many other places I would choose instead...A little Spain and a lot of Provence...sounds like fun to me.

Nice is about 3 hours each way from the Rhone Valley area. So, a long day trip that includes a lot of rail time.

Would you suggest a day trip to Nice, or is that too far? Depends where you're based in Provence. I've done Nice and Monaco as day trips from Aix-En-Provence. Splitting your time between Barcelona and the South of France sounds like a great idea. I think it would be expensive to take the train from Barcelona to Provence but you can take the Eurolines bus or a flight to Marseille(best option). The bus travels from Barcelona to Aix en Provence and Avignon.
http://www.eurolines.es/en/

The train from Barcelona to somewhere in Provence will not be that expensive. A bus would take a long time. A car is recommended in Provence and you would train to Nimes or Avignon to pick one up. If you buy your train ticket in Barcelona you can pay with a credit card for the Spanish train, but you have to pay cash for the French portion. Transferring from one train to the other is quick and easy. Going 2nd class is fine and less expensive.

How easy is it to travel around Provence with a car? We plan on doing day trips.

A car is recommended in Provence. Driving is not hard, and it's even easier with a GPS. I recommend you get the smallest car you can get away with to more easily navigate narrow streets and small parking spaces.

After two weeks in Provence you'll leave wishing you had more time. Get the Michelin Green Guide to Provence to see what's there and plan your trip.

Tex has said the magic words: Michelin Green Guide. They are by far the most complete for actual sights/sites to see, even if the pages aren't glossy and there are few photos.