Santiago de Compostela

I found many interesting places along the way. It's best to get a comprehensive guidebook that covers the northern part of the country and read about the attractions in each area. I liked all of the following. I'm mostly listing the larger places; there are many small towns that make attractive day-trips:

Galicia: A Coruna (on the coast)
Castilla y Leon: Leon and Burgos
Asturias: Oviedo (near coast) and Gijon (on coast)
Cantabria: Santillana del Mar (very small, very near the coast)
Basque Country: San Sebastian (on coast beyond Bilbao), Vitoria-Gasteiz

These places do not make a linear path; one would need to pick and choose.

Check for flights on Skyscanner.

Make sure you try to experience the distinct character of the autonomous regions you will pass through - Galicia >> Asturias >> Cantabria >>
Basque Country.
I'd go with a focus like this if you have a week.
Day
1. A Coruna & Lugo
2. Fishing villages along Asturian coast
http://www.spain.info/en/reportajes/villas_marineras_de_asturias.html
3-4. Oviedo
5-6. Picos de Europa mountains
http://www.spain.info/en/que-quieres/ciudades-pueblos/otros-destinos/cangas_de_onis.html
7. Santillana del Mar

TAP Portugal does fly from Bilbao to Lisbon directly.

What you see will depend on whether you take the northern or southern route. The towns along the northern route are mostly small towns while the southern has towns as well as medium to large cities. So, it really depends on what you prefer to see. All the towns and cities mentioned by others are nice. I'll add Ponferrada and Astorga to the list. So much to see, so little time. The roads in most of Spain are very well maintained.

If you choose the inland route via Leon, it could make for a quicker journey.

Day
1. A Coruna & Lugo
2. Ponferrada & Astorga
3. Leon
4. Burgos
5. Vitoria-Gasteiz