Museu Nacional dos Coches
Designed by Brazilian Pritzker Prize winner Paulo Mendes da Rocha, this very popular museum has a dazzling collection of gloriously gilded horse-drawn conveyances. The oldest on display was made for Philip II of Spain in the late 1500s; the most stunning are three created in Rome for King John V in 1716. The museum was originally located at the nearby Royal Riding School, which still has exhibitions. It's right next door to the official residence of the president of the republic, whose Museu da Presidência tells the story of the presidency, profiles the officeholders, and displays gifts that have been received on state visits.