Its in Nepal, at Gorek Shep (the last village you come to before Everest Base Camp). Altitude 5180m.
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If the hovels at Gorak Shep qualify as "hotels", then so do slaughterhouses in Purgatory! The hygiene is unspeakable at all of them, the toilets are usually frozen even in March, and various health agencies in Kathmandu have been urged to close down these "hotels" because so many trekkers have gotten very sick.
On the Everest trek, the highest elevation of a place that qualifies as a "hotel" is the Everest View Hotel, at an elevation of about 4,000 meters, about 13,100 feet, which is a quite nice place to stay. Perhaps there is a true "hotel" higher than that somewhere else on Earth.
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There is also a lodge in the Everest region though not on the Everest trek itself -- most guests get to this lodge by helicopter -- run by Yeti Mountain Home, called the Kongde Mountain Home. It is at 4,250 meters. I have not been there, so I am not sure that it qualifies as a hotel, though the web site makes it look very nice.
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Hotel Tayka del Desierto, Ojos de Perdiz in the Siloli Desert in Bolivia is at 4600m which makes it the highest in the world.
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