Southeast (?) France

How much of your 2-3 weeks do you want to spend going between the two places? What are your interests? What places do YOU really want to see along the way.

Collioure is a favorite of mine.

Check out Montpellier - a BEAUTIFUL mid-sized city.
Beyond that my favorite places are Pezenas - an old "village circulade" - amazing shops in this town since they give breaks on retail space to artists. Also a wonderful weekly market. Check out the nearby winery Abbaye de Valmagne in an old monastery...the giant wine casks fill the side chapels of the former church and they hold concerts in there during the summer months.
Beziers - for the cathedral high on a bluff overlooking the river. Take the stairs up to the top of the tower.
Narbonne - has a partially built cathedral that is unique. The town center is quite nice as well.
Collioure - a very picturesque seaside village with a beach bookended by a fort and a castle. The Fauvre artists loved this city for it's beauty and light. Unfortunately it IS on a lot of tourists lists but there is a reason for that!
St Guilhem le Desert - it's at the top of a canyon with a stunningly blue-water gorge. It's a pilgrimage town and very old. It's discovered but not totally overrun yet. At the foot of the canyon is a Roman bridge with a fantastic swimming hole underneath it...swim, rent a kayak, or just watch the crazy people jumping off of it into the water below!

"...cities to visit that aren't necessarily on everyone's list." I'm assuming that pertains to nearby small towns as well. I recommend Obernai as a day trip from Strasbourg or Colmar.