Please provide advice on my itinerary. Thanks!

If you can, fly into Bilbao.
Then car to:
Vitoria-Gasteiz
Logroño
Zaragoza
Train to Barcelona.

Skip Madrid and Bayonne.
Relax and enjoy life.

Madrid is a beautiful big city. That said, there are so many more interesting places in Spain than Madrid.

I would keep Bayonne. We liked it, and if you'd like to learn about the Basque culture, the Basque museum is excellent. Also the small surrounding Basque villages are really fun and very picturesque.

I don't see San Sebastian. We loved it. Very pretty city and "tapas hopping" was fun and some of the food really special.

We didn't get to Bayonne, but we fell in love with St Jean Pied de Port prior to our Camino walk. Zaragoza was nice... Not overrun by tourists -- but also not a bunch to see, assuming you're trip is to see castles and cathedrals. We liked it, though, and it's an easy train ride from Barcelona.

Consider driving from Zaragoza to Bayonne, then Bilbao, and drop at Logrono. That will take you through Pamplona and San Sebastian. (FYI, Le Tour de France started in Bliboa, went through San Sebsatian and Bayonne this year.)

Then take the train from Logrono to Madrid and Barcelona.

That route has you only repeat the route between San Sebastian and Bayonne. And it's a lovely route to repeat.

And if you choose to stay in St Jean Pied de Port -- again, we really enjoyed it -- I recommend the boutique place we stayed (I think just four rooms) Maison d'hotes E.Bernat... Terrific hosts... Their contact information:

Maison Ebernat
20 rue de la citadelle, 64220 Saint Jean Pied de Port, , FR
+330621328641
maison.et.bernat@gmail.com

I agree with @gbrennan in that your route could be more streamlined.

From Zaragoza go to Elizondo, in the Baztan Valley in Navarra. You can stop in Pamplona on the way from Zaragoza. Elizondo is about an hour from Pamplona. Spend a night in Elizondo, and then head up to Bayonne.

You can go the long way through Izpegui, down to Baigorry over to San Jean Pied de Puerto and then back over to Bayonne. Or you can go through the valley and cross the border in Dantxarinea. On the Spanish side you have the caves of Urdax and Zugarramurdi (where there was a famous coven of witches in the 17th century), and on the French side you have a lot of the lovely villages that @JulesM mentioned. If it is a sunny day I'd recommend the first one (the views from Izpegui on a sunny day are fantastic) and if it is more overcast/rainy I'd recommend the second one.

Going this way you don't have to repeat the coast stretch. Which as mentioned in quite nice.

If visiting Logroño is to visit wineries, you won't need the car for three day. Coming from Bilbao, you could stop along the way in La Rioja for a visit. The second day use the car to visit some of the sights in La Rioja, and then leave the car. The third day you can visit some of the wineries in town walking. Here is the tourist office's list.

While you can get to Madrid by train, the bus service is very good and usually faster and cheaper.