Ahead of a record-breaking travel boom, the capital’s best stays fuse futuristic comforts with artisanal touches—proof that Japanese hospitality is constantly being reimagined.

The Edge is a triangular observation deck 1,131 feet in the air that juts 80 feet out from the 30 Hudson Yards office skyscraper in New York City. To be sure, there are venues where you can score a ...