I always rent from Madrid’s airport. The rental agencies are right outside the terminal and getting onto a freeway only takes a minute. When returning the vehicle watch the return signs carefully. Right at the terminal when you turn in right by the return lot, you’ll need to turn right into the rental return lot. If you happen to go straight you’ll enter a pay lot. The signage is much better now than it used to be.
I like the itinerary. In Santillana Del Mar we stayed at one of the two Paradors there. The town is pedestrian only during the day, but if you stay at the Parador you can drive in to drop your bags. The Paradors have their own parking in the town.
Likewise, we stayed at the Parador in Olite. It too is in a pedestrian only zone but you can drive in to drop your bags, 30 minutes maximum. Parking is in a free public lot about a five minutes walk away. We visited Javier castle, the basilica beside it, and Monasterio de Leyre as a day trip from it. On another day we drove the area between Olite and Puente de la Reina visiting Artajona, Puente de la Reina, Monastery of Iranzu, the wine fountain on the Camino at bodega Irache, and Estella. A place we didn’t get to was Ujué.
Between Pamplona and Olite is Alto de Perdón. It affords good views of the surrounding area. Somewhat nearby is Church of Saint Mary of Eunate. Both places are on the Camino de Santiago so you will see pilgrims walking it.
If you need to do laundry by that point in your trip there was a laundromat near Olite, in Tafalla. Once away from Madrid traffic is very light. Just remember to stay at or below the posted speeds. There were free parking lots in places I mentioned. I looked them up before going over. Many of the places are in fairly remote locations so a rental car is a must.
When heading back to Madrid and if you’re in the area, Parque Natural Cañón del Río Lobos was a nice stop. Beautiful scenery and a Knight’s Templar built chapel (Érmita San Bartolomé) that is equidistant between the easternmost and westernmost parts of Spain. The partially walled town of Burgo de Osma was nice to walk around. There are a number of castles in that area too.