We are planning to drive from Barcelona to San Sebastian and have allocated about 5-7 days for this portion of our trip in late October. Any suggestions of what route to take, roads to avoid, good hikes, etc would be appreciated.
If you really want to see the Pyrenees, you need to do it from the French side where there are roads that parallel the chain rather than crossing them / going in and out of them as do the roads in Spain.
Draw a rough line from Perpignan to Bayonne and stay well south of it (as close to the border as possible) on the back roads. Even on these slow roads, it's easy to cover the whole route in two days, so you might have allocated too much time.
For hiking, a lot of people like the French national park. My preference is further east, either south of Prades or the area around Matemale. I've never had any trouble getting somebody to help me preposition a car for the end of the day. There are also plenty of loops (a bit longish, usually) you can work out if that's your preference.
Same answer I posted to the other pyrenees thread:
There is the Parque Nacional de Ordesa y Monte Perdido and the Parque Nacional de Sierra Y Canones de Guara. Both are not far from Jaca in the Aragone.
There is also the partial routes of the Camino de Santiago. One crosses the pyrenees going from St Jean Pied de Port in France to Roncesvalles in Spain, and another goes from Somport in France to Jaca in Spain (both carry "pilgrims" on their way to Santiago de Compostela). I know that there are hostel type facilities for pilgrims. I've no knowledge of mountain huts.
I've never hiked this area (Jaca), only driven. It's beautiful.
The Pic du Midi is the highest point in the Pyrennees along the Spain-France border. There is a lovely valley at its foot (French side) that you should include in your itinerary for sure: Vallée d'Ossau. Google it and you will find a lot of info about the hikes, the griphon vultures, the insular culture, traditional sheep herding, thermal baths, fabulous panoramas, a little steam train up the mountain, lakes and even donkey hiking.
http://www.valleedossau-tourisme.com/home/index.html?L=2
http://www.ane-en-rando.com/l_association_051.htm
I agree that the trip across is not as easily west to east on the Spanish side, as it is on the French side. This is what I would do: head from Barcelona to Andorra on the Spanish side. Then cross over to the French side, where hiking activities in the mountains are better supported with infrastructure, and the roads are slightly better. Then cross back along one of the previously mentioned traditional routes to Santiago de Compostela. My vote would be for Saint-Jean-Pied-de-Port, which also gives you the chance to go through Pamplona.
Hope this helps.