In mid June 2012 after walking to Finisterre I stayed two nights at Albergue Fistera (mentioned in Jochen-Schmidtke's attachment above - that's not the same as the Hotel Finisterre mentioned by Miguel). It was clean, quiet, very nice, included a full kitchen at a cost of 12 Euro per night (Oddly certain other people were charged 10 euro on the same nights. Perhaps I should have looked a bit more harried upon arrival or something). Pilgrims were provided with a key to the front door allowing for 24 hour access.
Although the albergue was not fully booked, as with many private albergues and contrary to what I read on one website, there was no requirement that one had to actually arrive in Finisterre by foot. Two women who were there at the same time arrived by bus from Santiago and stayed for five nights to unwind after their Caminos.