The city itself was organized into "calpullis", which are roughly equivalent to modern day city wards, with the important exception that each represented the basic political basis of the empire.

Out of the 20 or so calpullis that existed in the city, the central 8 or so belonged to the original Mexican settlers of the city with the others belonging to different ethnicities from around the empire (nahuatl and other, the mexica had a custom of establishing... lets call them colonies in conquered territory, with the explicit purpose of mixing with local groups), though nothing says that it wasnt possible (indeed we assume it was relatively common) for people to move from one to another.

Its also important to note that calpullis werent privately owned like in Europe, there wasnt a noble in charge of the calpulli, nor did they "belonged" to any governor figure, instead the calpullis were perceived as being communal property, nobody directly owned them or its terrains but rather it was the property of the calpulli inhabitants as a whole.

It was also important as I mentioned before the calpullis formed the basic political entity of the empire, meaning the people of the calpulli would elect its leaders, who in turn would elect the city's leaders, who in turn would elect the empire's leaders, a noted Pipiltlin (noble... kind of) could be awarded the rent of this or that plot of land from time to time, but he wouldnt "own" it, as it belonged to the people working it.

It is assumed that each calpulli would also house a school, either a Teposhcalli for the macehualli (commoners... kind of) or a Calmecac for pipiltlin (nobles... kind of) and a number of services like public baths, toilets, governance buildings, temples, would be swept in the mornings, etc...

The Altepetl (city) itself would have been ruled by a Tlatoani (king... kind of) who was directly below the Huey Tlatoani (Empero... kind of), tough in the case of Tenochtitlan, its day to day ruling was probably left in the hands of either the Huey Tlatoani or the Cihuacoatl (a Prime Minister of sorts... kind of).

Edit: Of note is also the nearby city of Tlatelolco, while technically a separate entity, the city, which was also founded by Mexicans entered a period of conflict with Tenochtitlan after the Mexica were expelled from Mexicaltzingo for wearing a Culhuacan princess's skin as a robe (long story), and was eventually conquered and almost annexed into Tenochtitlan proper, though this was never finnished and notably during the Fall of Tenochtitlan this was the last "section" of the city to fall.

---

Chronicle of Mexico; Alvarado Tezozomoc.

City Size in Late Postclassic Mesoamerica; Michael E. Smith.