You can certainly get a non-residents account with Banesto but they are a bunch of thieves quite frankly. If you left, say, 100eu in your account and checked your balance a month later, you'd only have about 48eu left. This is because they will charge you exhorbitant fees for having money lying in your account.
Spanish Barclays are good, as are Bancaixa (La Bancaja). I'm just not sure if they do non-residents accounts as I was officially resident by the time I opened accounts with them.
Contact one of the ex-pat newspaper companies via email and they will probably give you more helpful information. Best of luck.