Perched on a hilltop overlooking the Pacific, Mexico’s Casa Cuixmala resort endured the worst of Hurricane Patricia’s wrath last fall. The storm was the second-most intense tropical cyclone ever recorded, with winds reaching upwards of 150 mph when it made landfall.

Now, after months of renovations, the 25,000-acre, 11-year-old resort has reopened its seven private villas. Ranging in size from 1,400 to 2,500 square feet, each bungalow now boasts vibrant, locally sourced fabrics; an expanded outdoor terr…