Popayán’s best hotel is set in a 16th-century Franciscan monastery adjacent to the Iglesia San Francisco. Despite being taken over by the upscale Dann chain, the hotel’s historic architecture has been preserved. Throughout the property are fine hand-carved woodwork, gold-framed oil paintings, and elegant chandeliers. The rooms, which have carpeted floors and are decked out with antique furnishings, wrap around a huge stone courtyard. Some add furnished balconies, and suites have dining areas. The sprawling grounds, with beautifully manicured gardens and an outdoor pool, make the property feel like a city within the city.