Hotel Panache, located in Paris's 9ème, near the Folies Bergères cabaret, is in a historic corner building that says designer Dorothée Meilichzon, "has an unusual shape for Paris, it's an acute angle. " Its proportions led it to be compared to New York's Flatiron building and inspired Meilichzon to reference that era. And to deploy geometric shapes and patterns throughout. The results pack a lot of punch—and somehow all work. Rates start at a reasonable €120 ($140) a night.