The city's historic center is the Plaza de la Constitución, or Zócalo. The plaza was paved in the 1520s by Hernán Cortés, using stones from the temples and palaces of the Aztec city of Tenochtitlán he'd destroyed, and on which Mexico City was built. The original Aztec city was on an island in the middle of a lake, so many of Mexico City's older buildings and churches are sinking into the boggy ground on which they were constructed. Filling the entire eastern side of the Zócalo is the Palacio Nacional (National Palace), built on the site of an Aztec palace and formerly used to house the viceroys of New Spain. It is now home to the offices of the president and a museum devoted to the life of Benito Juárez, but most people come here to see Diego Rivera's fabulous murals, which chronicle Mexico's history.
The Aztecs' sacred precinct stood on the huge site now occupied by the Catedral Metropolitana, on the northern side of the Zócalo. The cathedral was built between 1573 and 1813 on the site of the Aztecs' tzompantli (an altar of sorts on which the skulls of the sacrificed were placed). Just east of the cathedral are the remains of the Templo Mayor, the Aztecs' principal temple. Much of the site has been excavated, revealing the temple's multiple layers of construction and the extraordinary bloodiness of the rituals that took place there. An excellent museum displays artifacts discovered during the excavations.
Less than a 10-minute walk away is the Alameda, once an Aztec marketplace and now the city's largest downtown park. The streets around the Alameda are lined with the city's most interesting buildings, including colonial mansions, lively cafes, restaurants, shops and markets.
Other must-sees include the Bosque de Chapultepec, Mexico City's largest park and home to museums, lakes, a zoo and the official residence of the president; the Basilica de Nuestra Señora de Guadalupe, the church built on the spot where Mexico's patron saint was seen in a vision; the colonial houses, cobbled streets, fabled craft market and Rivera-Kahlo related sites of San Ángel; and the ancient canals of Xochimilco, jammed with day-glo pleasure boats on weekends. The Zona Rosa is the city's major highlife and nightlife district. Condesa and Roma to the south of Zona Rosa also serve up good food and entertainment. The best moderately priced hotels are found in the areas west of the Zócalo and south of the Alameda. Excellent cheap food can be found in most areas of the city, particularly from street stands and comedores.