As I recall, Tolkien described Faery as being the realm where the creatures of faery (eg, elves, dragons, dwarves, leprechans, paladins, talking trees, etc, etc) live and exist in their natural place. {I apologize in advance for the crudity of my recollection, Tolkien put it far batter than I just did}. Faery stories, then, were stories about interactions between normal, mundane "people" and denizens of "The Perilous Realm".
- The Middle East, with its Genies may be on the borders of Faery - for all that it is mostly desert.
- Greece, with its Centaurs, Minotaurs, Fauns, Satyrs, Cyclops, Sirens, etc seems VERY "Faery" to me.
- UK (especially Ireland) with its fairies, leprechans, and so forth, is (for one grown up in Northern European traditions) quintissential "Faery".
But Egypt - I don't think it's so much the climate as it is I am not familiar with much of any "faery" elements in Egyption history or mythos. That coul be because there aren't any, or because I am just ignorant enough of Egyption mythos that I don't know they are there.
Either way, a place isn't going to "feel" faery, unless one is consciously aware of the denizens of faery residing in the place - or, at least, visiting it from time to time in the stories of the place.