There’s a huge hotel there, the Inn on Fogo Island, it’s a 3 night minimum stay and will cost around $1000 Canadian per night, but for that you get all your meals and a bunch of other stuff.
You can just see it in the distance between the power poles. Of course we didn’t stay there, we stayed in a salt box house B&B just down the road, we got great food and coffee at Bang Belly in Fogo itself and just looked at the hotel as we passed now and then. To be honest the whole point of the place is to benefit the people of the island, it’s a not for profit thing that ploughs it’s surplus cash back into making the fabric and the people of the land better than it could be.
Fogo Island itself is almost unworldly, bleak, barren, and unforgettable in a beautiful way, even in a howling gale with rain and 4f. temps There’s lots to see, quite a few places to stay and the people are just so warm and friendly. Take outdoor gear and be prepared to rough it a little and you’ll be just fine. A great experience on the ferry too, you only pay one way so the return trip is in effect free.