The largest city of the Aztec culture was called Tenochtitlan, located in what is now Mexico City. Mexico City is one of the largest cities in the world, and it is in a very odd place for a capital city; on a marsh in a lake bottom ringed by mountains, and prone to earthquakes and some of the worst smog on the planet. How the Aztecs selected the location of their capital in this miserable place is part legend, part history.
Tenochtitlan was the home of the immigrant Mexica, one of the names for the Aztec culture people who founded the city in AD 1325 on an swampy island in the middle of Lake Texcoco, in the Basin of Mexico. According to legend, the Mexica were one of seven Chichimeca tribes who came to Tenochtitlan from their fabled city of origin, Aztlan (Land of the Heron). They came because of an omen: the Chichimec god Huitzilopochtli, who took the form of an eagle, was seen perched on a cactus eating a snake. The leaders of the Mexica interpreted this as a sign to move their population to an unpleasant, miry, buggy, mess; and eventually their military prowess and political abilities turned that mess into the central agency of conquest, the Mexica snake swallowing most of Mesoamerica.
Aztec Culture and Conquest
Tenochtitlan of the 14th and 15th centuries AD was excellently suited as a place for the Aztec culture to begin conquest of Mesoamerica. Even then, the basin of Mexico was densely occupied, and the island city afforded the Mexica commanding lead over trade in the basin. In addition, they engaged in a series of alliances both with and against their neighbors; together the Triple Alliance overran major portions of what are now the states of Oaxaca, Morelos, Veracruz, and Puebla.
By the time of the Spanish conquest in 1519, Tenochtitlan contained around 200,000 people and covered an area of five square miles. The city was crisscrossed by canals, and the edges of the island city were covered with chinampas, floating gardens. A huge market place served nearly 60,000 people daily, and in the Sacred Precinct of the city were palaces and temples the like of which Hernan Cortes had never seen. Cortes was awed; but it didn't stop him from destroying almost all of the city in his conquest.
Remnants of the Aztec Culture
Only parts of Tenochtitlan are extant in the city of Mexico; you can get into the ruins of the Templo Mayor, excavated beginning in the 1970s by Matos Moctezuma; and there are ample artifacts at the National Museum of Anthropology in Mexico (INAH).