I would certainly recommend Donostia - San Sebastián (to use the new official name) as a weekend visit, it has good Basque food options, some excellent independent hotels, a good range of shops and one of the most impressive in in-town beaches.
The airport is a little way out of town, it's actually on the border at Irún, on reclaimed land at the docks. Any further over and in would be a French airport. It will be an interesting landing/departure experience, given the LCY landing at the other end. It's conected to D-SS by public bus, and there is a regular coach service to and from BIO airport too. EAS has services to MAD.