I would suggest Avignon as the best place to stay. They have a TGV station, the pope's 1300's Palace, and some great restuarants, and you can do easy day trips to Nimes, Pont du Gard, Aix en Provence, Les Baux, Arles, Orange, .. maybe even Rousslon or Gordes. Avignon has nearly complete city walls in tact, and a famous bridge. Its just the ideal size - not to big, not too small.
Lyon is kind of a mini-Paris but walkable. The restaurants are good but most seem to serve the exact same menu. There is a funculur to the mountain peak and a beautiful church. And a WWII museum. We also dealt with pickpocketing teens in Lyon. The last time we went, we spent 4 times the price on hotels as we did on Avignon for a lousier place.
Narbonne is a nice but quiet place. Its 45 minutes from Carcassone which would be worth a visit. Narbonne is cute and quiet. There is a nice little river area. It was also the capitol of the Roman province around the name of Ceasar, and they have some Roman ruins in small quantity there.