The Convent of São Francisco was founded in the 16th century and expanded through the Baroque period, eventually becoming one of the most substantial religious complexes in Angra. After the religious orders were suppressed in Portugal in 1834, the building was repurposed and now houses the Museu de Angra do Heroísmo — the main museum covering the city and island's history. The conversion has been done thoughtfully; the cloister in particular retains much of its original character.
The museum collections span pre-history through the 20th century, with particular depth in the Age of Discovery period when Angra was a critical Atlantic waypoint. Navigation instruments, maps, trade goods, and documents from the 15th through 17th centuries occupy a substantial part of the collection. There's also significant material on the island's role in the Portuguese Liberal Wars of the 1820s-30s (Angra backed the Liberals, which is how it acquired the "Heroísmo" part of its name). The cloister garden is one of the quieter spots in the city — worth pausing in even if you're moving quickly through the museum.