San Sebastian has an airport, but it's just for Spanish and French local flights iirc. There are hotels near Bilbao airport, but to be honest it's a quick spin into the city, where you'll get a better hotel and a chance to see the sights.
I'd arrived in Bilbao on a delayed aer lingus flight, with only one flight left to arrive into the airport, and managed to taxi into the city, check into the hotel, and then grab a few tapas in the old quarter.
There's a regular bus service from Bilbao (get the tram that goes out of the city centre by the Guggenheim to it's terminus - that's the bus station) to San Sebastian, but when I got it, it didn't go via the airport (though it passes nearby).