Not sure if that's the correct translation but I think he means an inn. Basically what I understand as a Gasthof is something like a restaurant which also rents out some rooms.
yeah inn is probably the best equivalent in english, most of the time a gasthof is just the right scale of establishment.
It's small enough that it's cheap and cozy, but large enough that you actually have decent rooms and service.
Plus you can find a gasthof in really small villages in germany, it's so much nicer than staying at a hotel IMO.