Are there any cider houses or place that only serve cider in these two cities? Or are there any nearby within a reasonable bus or taxi ride?
Cider farms are, obviously, in the country and you need to drive to get to them, some are also available on public transport. The most famous and real ones are around Donostia-San Sebastian, in Hernani, Astigarraga, Urnieta,..., and they only serve cider but only as part of a fixed menu. Cider is served directly from huge barrels in the middle of the dining room, and you cannot do it directly but it´s somebody from the "sagardotegi" or cider house. There´s one in Bilbao, called https://bilbaosagardotegi.com/ , but it´s not the real thing (there are others in Donostia-San Sebastian, but again, it´s not the real thing). By the way, expect a light drink, 6º alcohol, not too sweet, not carbonated and quite different from cider in other countries. If you happen to visit one on a weekend from Jan to May, there should be lots of local atmosphere, music, singing, dancing...but make a reservation first.
Not sure what you mean by "only serve cider", but we went to the Sideria Intxaurrondo in San Sebastian.
We're looking for places that specialize in cider, not just a bar or restaurant.