our flight arrives in San Sebastián at 7:40am but we can't get keys to the apartment we rented in the old town until 9:30. I thought we could find somewhere to have breakfast but wondered if there is somewhere we could store our luggage?
Hondarribia, the town closest to the airport, has a charming, historic hill-town core, worth visiting. But the airport doesn't advertise any bag storage, so you'd probably have to ask nicely at cafe, etc. I was going to suggest taking a short taxi ride from the airport to the tourist information office on the main square and hope that they would hold your bags, but that office doesn't open until 10:30, even in high season.
If you're heading straight to San Sebastian, the express bus E21 takes half an hour.