Another vote for Barcelona. Then drive To Andorra for the duty free shopping. The Pyranees are beautiful but you don't get far in a day.
Madrid looked as I imagine Moscow would look and, while others may know better, El Prado art gallery was all I found.
Not far out of Madrid on the way to Valencia is Quenca. A gem! We made the mistake of spending the day or so in Madrid before hiring our car and got hopelessly lost before we got outa' town. Grab the car at the "airporto" and head out of town towards the Mediterranean and it is only a couple of hours drive. Stay at the Hotel Exucar. Next to it was (is?) a cafe where we had our first sangria. We stayed an
extra night the place was so good.
'Tis a long time since I was there and they may have changed but the Paradores are worth looking at for accommodation. Every one is unique in some way and they weren't outrageously expensive.
Toledo was an interesting city and the Parador there had a vista down the valley.
I can think of more but in general I liked the north.
ps. How much I would have given for a GPS.
Edit: While it is pronounced with a "Q" the spelling is "Cuenca".
Don Bourke did a TV special on the Alhambra. So popular now that you have to book in advance, apparently. Don't even think about finding your way in without a GPS.