Budapest’s plentiful thermal springs gush mineral-laden waters that are both a geological wonder and an invitation to partake in a restorative, distinctly Hungarian ritual. The City of Baths, also known for its rambunctious ruin bars, has for centuries beckoned travelers with a salve for their ailments. But beyond purported curative powers, these historic bath houses also mesmerize with a transportive Old-World ambiance—balmy pools backdropped by splendid architecture create soothing interludes in Baroque, Art Nouveau, and Renaissance-Revival settings.