Panarea, a island just north of Sicily. The small island is volcanic and the architecture had a byzantine feel to it. I started looking in areas that matched it.
Then I looked at the tile work, and focused on that a bit, and found a larger picture with a blue door.
Blue door hotels are all over the place in Panarea. It's very, very common.
At this point, if I was trying to locate a hostage (I do this as a hobby, this is OSINT), I'd Google Street View every street, comparing building to building to the exact viewing angle of this image to the island out in the water, until I was sure I had the place and would send it to the national agency that deals with that stuff. I'm not gonna waste that time on this, as it is a crazy expensive place to visit and you'll never be able to afford this precise room, and it undoubtedly has one hell of a waiting list. The island is a tourist trap.
I'm positive I got the right island, I've seen about 40 different angles of that island in your pic. There is also another pic from a tourist:
I can't download it so I just screen shot it. They have a bunch of old weathered antique chairs at this resort.
