Public laundry. Not too often to see it in Budapest anymore though in the 60s it was quite common here too. Its not a self-service system there is a staff that handle your cloths and other materials. People usually bring there suits or special clothes.
Cool. I never thought such a thing existed in Budapest. What your describing is called a dry cleaner here in Canada. We also have laundromats here too. Laundromats are self service however.
It looks like a much nicer laundry at least from the outside than many of the places here!