The Palacio de San Agustín, originally built as a residence for a Spanish miner in 1675, was transformed in 2008 into a museum hotel—the first of its kind in Latin America. It’s now home to more than 500 pieces of art, mostly centuries-old paintings from Germany, Italy, and France. While the collection is impressive, what’s also of interest here are the building’s original architectural elements: an exquisite chapel (used primarily during the house’s stint as a convent for the Order of Saint Augustine), stained-glass windows and doors, parquet wood floors, and a spiral staircase. A secret entrance leads to an underground tunnel—once part of a large network of covert walkways that connected the city’s major churches and affluent residences—that now opens up to an elegant wine cellar and an old cistern, and links up to an events space across the street. Have time to linger a bit? Stay for a glass or wine or bubbly, served in a chic lobby outfitted with antique French furnishings, or on an expansive rooftop terrace with sweeping city views.