I highly recommend the basque country, especially if you are looking for food, drink, and relaxation.
Madrid was ok, we spent like 2 days there. It's just a European capital, not terribly unique. Good museums, food, and nightlife, but not mindblowing.
We spent our time in the basque country primarily in San Sebastian. The food is amazing. We ate at Arzak which is the best meal I've ever had and quite an experience. The pintxo bars in town have great food as well, and there's a shitload of bars in San Sebastian. The beaches in SS are solid. There are some great surf breaks nearby if you're into that.
We also made a day trip to Biarritz, FR (45 minutes by car) one day which is where I would live if I had to choose somewhere in Europe to live. Surf break right in town, great cafes, beautiful scenery and relaxed vibe. Quick stop in Hondarribia on the way was worth it (walled medieval town right on border).
Bilbao was underwhelming. If you really want to go to the Guggenheim than fine, but otherwise I'd skip it.
You can also check out the Rioja wine region pretty easily from there, maybe do an overnight trip. There's probably a ton of cool towns we didn't get a chance to see.
I've never been to Barcelona or Andalusia. My wife had been to southern Spain and said the basque country was a totally different experience. The landscape is green and rugged (think northern CA/Oregon) vs. southern Spain's San Diego/Baja resemblance.
Weather in may was decent. We had some rainy days and some nice sunny beach days, temps ranged from about 60 - 75 F for daytime.
I don't have anything else besides Madrid in Spain to compare the basque country to, but I highly recommend it for exceptional food, drink, culture and a unique experience.