Madrid-San Sebastián drive - stops along the way?

A few options I thought of. Many are in out of the way locations, but not far from main roads.

Castillo de Pedraza, Burgos, Castillo de Sajazarra, Monasterio de Santa María de la Piedad - Madres Dominicas, Cihuri- Puente Romano Siglo l, Haro, and Ermita de la Purísima Concepción (San Vicentejo).

Going another route: Mirador Alto Del Perdón, Iglesia de Santa María de Eunate, Puente Románico de Puente la Reina, Monastery of Iranzu, Iglesia de San Pedro de la Rúa and Weevil bridge in Estella, Pamplona, Logroño, Soria, Almazán, Roman arch of Medinaceli, Sigüenza, Cascada del Gollorio near Sigüenza, Guadalajara, Alcala de Henares.

Edited: if you decided to visit Trasmoz as suggested by Carlos, nearby is the Convento de las Concepcionistas Franciscanas / Sor María Jesús de Ágreda. Known as the Blue Nun for her habit, she was a noted mystic in her era. She was known especially for her extensive correspondence with King Philip IV of Spain and reports of her bilocation between Spain and its colonies in New Spain. She is entombed inside the convent.

All good places that Jaime mentioned. I really like the Monastery of Iranzu. It is about 15 mins of the highway, nestled in a hidden valley. Chance are it will be cooler than a lot of other parts of Navarra in August.

I would add, if you are going the San Sebastian-Pamplona-Logroño-Soria-Madrid route, Numancia. It is just north of Soria and was the scene of an historic resistance to the Roman Legions. It is just off the N111.

Also on the route through Burgos you have Vitoria-Gasteiz with its large, hilltop medieval district. But this is a city, as is Burgos, and you might prefer to combine Burgos with one of the smaller towns if you have time for two stops. You'd almost certainly waste less time dealing with parking that way. You can kill a lot of time in Burgos just with the cathedral and wandering around, looking at the architecture.

If you zoom way in on the route maps provided by ViaMichelin.com, you'll see the most scenic roads outlined in green. I didn't approach the Basque Country from Madrid--or by car--but I remember thinking there was a lot of lovely countryside in the Basque Country. You'll see a lot of green on the ViaMichelin maps.

Laguardia isn't on one of the route options outlined by ViaMichelin, but it's on a secondary road connecting two of the routes. Laguardia is a very atmospheric hill town, roughly between Vittoria-Gasteiz and Logrono. There's parking below the town, I believe; there's definitely an elevator up to the top. The road from Laguardia north is one of ViaMichelin's green roads.

The side road heading north out of Estella looks promising scenically, too.

Alternatively, if you take the A-15 route north that goes through Pamplona (5 hr 15 min) or maybe on your way back, there are two unique stops I'll suggest:

Trasmoz - a cursed village of witches and dark magic, Trasmoz is the only town in the world to be excommunicated by the Pope. Tucked in the foothills of the haunted Moncayo mountain range, Trasmoz has centuries of witchcraft history. For example, a deadly epidemic struck the village in the 19th century and a quiet woman was suspected of causing the disease and thrown into a well! You can read more here - https://www.bbc.com/travel/article/20160418-spains-cursed-village-of-witches

Olite Royal Palace - a fortified medieval town with winding narrow streets and impressive old walls. Don't miss the Royal Palace of Olite, the seat of the Kings of Navarre, actually incorporated into the old town's fortifications. For me, it's one of the more impressive medieval castles in Europe.

Under-visited Olite is a great contrast to the mob scene one usually (though quite possibly not this year) encounters in San Sebastian. I found it not overly blessed with restaurants, so if you anticipate stopping there for a meal, I'd suggest some online research ahead of time.

If you take the A15, it will also lead to Soria.

One town you will pass close by is Tarazona. I'm sure @acraven can talk it up.

Also you would go through the town of Agreda. There is a convent there with the incorruptable body of Sor Maria de Jesus, a 17th century nun/mystic who bilocated and appeared to the native americans in New Mexico/Texas area. The Texas blue bonnet is supposedly named after here as she appeared wearing a blue bonnet and the flowers appeared after her visits.

I did like Tarazona, but the details have been lost in the mist of time; I was there in 2016. It's a picturesque town with very, very few tourists--my favorite sort of place. Here are some photos from the internet (not mine):

https://www.bing.com/images/search?q=tarazona+photos&qpvt=tarazona+photos&form=IQFRML&first=1&tsc=ImageBasicHover

Puente La Reina: https://www.google.com/maps/dir/Madrid,+Spain/Puente+la+Reina,+Spain/San+Sebasti%C3%A1n,+Spain/@41.8475308,-4.916831,7z/data=!3m1!4b1!4m20!4m19!1m5!1m1!1s0xd422997800a3c81:0xc436dec1618c2269!2m2!1d-3.7037902!2d40.4167754!1m5!1m1!1s0xd50879512bb724d:0x689d5755efe787f6!2m2!1d-1.8135943!2d42.6723037!1m5!1m1!1s0xd51affe3b68fe15:0xe43ec55994864649!2m2!1d-1.9812313!2d43.318334!3e0