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Photo: Diego Delso, CC BY-SA 4.0 via Wikimedia Commons
This museum presents the history of the city in an 18th-century mansion; the building is possibly more interesting than the contents. It is believed that a conquistador's house used to be on the site, as evidenced by the southwest cornerstone of an Aztec serpent head likely taken from the Templo Mayor.
The Museum of Mexico City is located at Pino Suarez 30, a few blocks south of the Zocalo, on what was the Iztapalapa Causeway, near where Hernán Cortés and Moctezuma II met for the first time. This building used to be the palace of the Counts of Santiago de Calimaya, who were the descendants of one of the conquistadors with Cortés. The house was extensively remodeled during the colony to much the appearance that it has today and remained in the family until 1960, when the Mexico City government acquired it from them in order to found the Museum that is found there today. The museum contains a number of elements of the old palace as well as 26 rooms dedicated to the history and development of Mexico City from Aztec times to the present. It also contains a library and the studios of painter Joaquín Clausell, who lived here in the late 19th and early 20th centuries.
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Supreme Court of Justice of the Nation
This building was completed in 1945 and was designed by architect Antonio Muñoz Garcia.
Plaza de Tenochtitlán
This place is allegedly where the Aztecs found the eagle eating a snake on top of a cactus (nopal), the divine sign of the gods to settle down and establish the city of Tenochtitlán. It features a sculpture by Juan Olaguibel made in 1970.
National Palace
The palace in its current form began construction in 1693 and served as the Palace of the Viceroy of New Spain until the Mexican War of Independence, when it became the executive seat of the President (though today it is no longer his official residence). The walls inside the palace display murals by Diego Rivera depicting the history of Mexico from the pre-Columbian age to the Mexican Revolution. You can also visit the Recinto Legislativo, a replica of the first Mexican Congress, and tour the home of Benito Juárez. Tours in English are free; ask for one at the information desk across the street. It’s strongly recommended to get there early in the day, and you’ll likely be given a reserved time to return later that afternoon.
El Zócalo
This square measures 240m long on either side. A huge Mexican flag occupies the center, which is ceremoniously lowered and re-raised each day at 18:00. You may see art exhibits, concerts, demonstrations or all manner of social gatherings taking place here. On New Year's Day, practitioners of Mexico's indigenous religions gather to bless believers for the coming year; Mexican independence is celebrated in the plaza on 15 and 16 September. During December, through the miracle of modern refrigeration, the entire Zócalo is transformed into an ice skating rink.
National Museum of Cultures
Housed in the former Mint building built in 1734. The museum is dedicated to anthropology of the world.
House of the First Print Shop in the Americas
This building, which dates from 1524, housed the first printing press in the New World, which operated from 1539 until 1560. After this time the building was used for a number of purposes until it was restored by the Universidad Autónoma Metropolitana (UAM) in 1989; it now houses a museum displaying some of the first books printed in Mexico.