Rick covers some highlights of the Basque Country (French as well as Spanish) in his guide book to Spain.
Lunches in Spain are late, the locals starting around 2 PM, so you'll be happy with the pace of life. And it will be great to have enough time to really explore this very interesting area. The Spanish-Basque countryside is very pretty; I've seen less of the territory on the French side of the border.
It's pretty much always rainy season in the Basque Country, but Pamplona may be far enough south to be in a different weather zone. The areas closer to the coast have a lot of overcast weather even when it's not actually raining. That makes it a good place to go when it's uncomfortably hot in most of the country, but it may (or may not) be surprisingly cool.
I'm not particularly fond of Pamplona, whose main claim to fame is the Running of the Bulls. It does have a smallish historic area, and I enjoyed spending 4 to 6 hours seeing the sights, then I was happy to move on. It is quite touristy because of the Festival and Hemingway's writings. It wouldn't be my choice of base; I preferred Vitoria-Gasteiz, Laguardia and Olite, which are very different from both Pamplona and each other. Vitoria-Gasteiz is the capital of the inland area of Alava; it is very seldom visited by foreign tourists and has a great medieval district on top of a hill with outdoor escalators providing assistance in getting to the top. There are also a few museums. Laguardia is a cute-as-a-button medieval hill town (elevator to the top) near the La Rioja wine district. I think you've made a good choice in Olite; the castle is impressive, and the town has a forgotten air that makes visitors feel like it's their own discovery. I'd pay attention to the location of your Pamplona lodgings and the parking situation so you can get in and out of town for day-trips easily.
St-Jean-de-Luz is a very picturesque place but fairly small. I spent a lot more time walking around the historic parts of the larger Bayonne, which I would definitely recommend seeing. Bayonne also has potentially interesting museums (including the Museum of Chocolate run by Atlier du Chocolate, with its extremely generous tasting room). Biarritz I didn't particularly care for (it was raining persistently, which didn't help), but some enjoy its grand-old-resort atmosphere. However, I i very much liked Biarritz's privately-run museum of Asian art, whose major focus seems to be the decorative art of southern Asia.
I didn't have a car and didn't make it to any of the mountain villages of the French Basque Country; I imagine you plan to do that.
The trio of former fishing villages (Zarautz, Getaria, Zumaia) is picturesque, but they are quite small places. You won't need long to see them, and Zarautz is only a 20-minute drive from San Sebastian (according to ViaMichelin.com). I wouldn't choose Zarautz and San Sebastian as two separate bases so close together, and 8 nights seems a very long time in that very limited area. I think you may want at least one additional night on the French side of the border.
San Sebastian has a lively (read: extraordinarily touristy), smallish historic district full of restaurants and tapas bars (not my scene at all, but I assume most people who go there love it). There's a good museum, and the walk along the seafront gives a great view of the spectacular bay. I'm one of those who much preferred the larger, less touristy Bilbao. Bilbao's historic area, the Casco Viejo, is larger and much less touristy. Plus there's the art.
Hondarribia, which sits very near the French border, is a good day-trip from San Sebastian, or you might visit it on the day you transfer from France back to Spain, assuming you are comfortable with the security of your belongings in the trunk of your car. The fishermen's district along the waterfront is full of restaurants; the medieval district is uphill.
