My husband and I will be doing the Camino De Santiago this summer, 10 days, 20 kms a day. At the conclusion of our trek, we are planning on renting a car and driving to Vigo, back up to Cee, Fisterra, then drive along the northern coast (stopping in La Coruña, Oviedo, Gijon, Santander, Bilbao) all the way to Pamplona. Any suggestions on places to eat and stay? Things to do? Should I plan the routes or just "play it by ear"? We have 5 days to complete this "tour".
Pick up a guidebook that covers northern Spain, because there is a lot to see in the area.
I haven't been to Cee or Fisterra, but I hit the other cities you mentioned this year, booking hotel rooms 1 to 3 days in advance in most cases. Vigo is underwhelming, in my view, and could be skipped unless you have a special reason to go there. I preferred Pontevedra in that part of Galicia.
A Coruña has a nice old quarter that I enjoyed a lot. The city has an annual jazz festival. This year it was in July. At least some of the concerts are outdoors (in the old quarter) and free. Gijón (also spelled "Xixón") is host to the annual Semana Negra literary festival (I think Spanish only). It focuses on thrillers. The 2016 dates were July 8 - July 17. In both cases, hotels might be pricier than usual during the festivals.
Otherwise, I think Gijón--primarily an industrial city--doesn't get a great deal of tourism except from boaters (so may not have too many hotels?), but I enjoyed my afternoon walk-around. There's a historic district plus some quite attractive early 20th century architecture in the nearby "downtown" area. I would have liked to have a full day there, just for walking around and looking at the architecture. Young folks from Oviedo go there for the nightlife.
Along the coast between A Coruña and Gijón, I enjoyed the picturesque towns of Betanzos and Cudillero. The latter is quite small, and I'm not sure where you'd park your car. Most such towns have a historic church or two, but I basically just wandered around.
East of Gijón you have Ribadesella, Comillas (some modernista architecture) and (barely inland) the charming, medieval Santillana del Mar. The latter is absolutely worth a stop despite all the tourists. There are caves with prehistoric art nearby, though these days you may be limited to seeing reproductions. If you're interested in the cave art, research it in advance and make the necessary reservations.
Santander is a pleasant city, attractive enough but rather modern because of a catastrophic fire in 1941. It has large sandy beaches. Otherwise, I found it less interesting than many other cities in northern Spain. It is, however, a decent jumping-off point for the dramatic Picos de Europa to the south. This is an area that's difficult to see without a car. Since you have a car, I hope you will find time to drive through the stunning mountains and gorges there. Potes is a charming old stone town built along a river. It's popular with the active-tourism set so probably would require a hotel reservation made in advance for a summer visit.
Oviedo has a handsome historic district, but it also has several very important (UNESCO-listed) pre-Romanesque churches located elsewhere in the city. You could very easily fill a full day in Oviedo, or more.
In Bilbao, in addition to the Guggenheim, the Museo de Bellas Artes is considered quite good. The old town is a healthy walk from either of the museums, but there is also public transportation available. It's very atmospheric and could occupy several hours. The newer part of the city is quite handsome, with lots of nice early 20th century buildings.
Should you find yourself approaching Bilbao with more time than you think you'll need for that city, I recommend a visit to Vitoria-Gasteiz and/or Laguardia in the Álava section of the Basque Country. V-G is sizable city on the way to Pamplona. It has a large historic district charmingly termed "the medieval almond" because of its shape. There are several worthwhile museums. Closer to Pamplona, Estella and Puente la Reina are worth a quick stop if you have time.
Weather-wise, of the cities on your list, there's a good chance A Coruña will be the warmest. Be prepared for clouds, dampness, and fog from time to time.
In Spain it's definitely advisable to research restaurants ahead of time. I encountered a lot of mediocre food.