UZBEKISTAN – “Wait until we get to Khiva,” my Uzbek friend Otabek Saidov whispers whenever I gush over the country’s beautiful sights, as he takes my sister and me on a tour of the country.

One of the major palaces, Kuhna Ark, has cool rooms laid with blue and white tiles and a mosque resplendent with an orange-gold ceiling that makes you want to stare at it in awe. Khiva is a town ...