Photo: miguelão, CC BY-SA 2.0 via Wikimedia Commons
This excellent four-story museum was designed by Mexican architect Pedro Ramírez Vázquez, and built in 1987 to showcase the many artifacts found on the site. Highlights include the Coyolxauhqui disc as well as the many thousands of offerings found during the still-ongoing excavation.
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The site of the main Aztec temple of Tenochtitlan, it was destroyed by Spanish conquistadors in 1521, who then promptly erected the Cathedral roughly over it – but not quite. Centuries later, nearly completely forgotten, its actual location was discovered by accident in 1978 when electrical workers found a piece of a large stone disc depicting the goddess Coyolxauhqui. This set off a few furious years of archaeological digging, resulting in a rather surprising (and extremely significant) discovery that nested underneath the original Aztec temple was six distinct smaller, older temples. You can see each layer walking through the dig site.
Iglesia de Santa Teresa
Built in 1678 and refurbished in 1845.
Antiguo Colegio de San Ildefonso / San Ildefonso College
Managed by the National University, this museum features some stunning murals and hosts great permanent and temporary art exhibits.
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.
Antiguo Palacio del Arzobispado
Eclectic art collection owned by the government's Finance ministry. Mexico has an innovative tax program that allows collectors and artists to pay tax debts by donating significant artworks. The collection includes works by famous artists like Diego Rivera, Frida Kahlo, and Rufino Tamayo as well as many cutting-edge contemporary works.
Museo JLC / José Luis Cuevas Museum
Housed in the former convent of Santa Ines built in 1600. The museum's collection features works by Mexican artist Jose Luis Cuevas as well as other modern artists, it also presents works (especially sculptures) from European artists such as Picasso and Rembrandt. The museum's courtyard features an enormous statue called, appropriately enough, La Gigantesca.