Given the nature of the city I would assume Tenochtitlan would have been largely wood and thatch buildings, and rural villages I would also assume would be similar, or built from whatever was on hand. But would some place like Texcoco, Caracol or Cholula have been filled with wooden structures too? Or would they have used something more like brick and stone, maybe covered in adobe or plaster? All my attempts to look for what their day-to-day structures look like just give me the temple complexes or modern day rural native villages, nothing about what your regular Joe Schmoe might have lived in if he lived in a city.
Maya archaeologist here. They would mostly have looked something like this: https://images.app.goo.gl/g7B3qusnHvhCwZNv5
Low stone foundation with a building made from pole and thatch. In some areas buildings with bajareque (mud and plant material, akin to adobe) walls were also very common. The all-stone buildings you see at archaeological sites were incredibly rare and limited to elite residences or public structures. In a lot of cases, even massive temples had perishable buildings on top of them. When you go to a site and see a huge pyramid without a stone superstructure on top, it's generally a safe bet there was a pole and thatch building up there back when it was in use.
Edit: I just realized the link I provided shows a building with bajareque walls, but you also get to see the pole beneath it pretty clearly. In lots of cases it's just the poles without the bajareque.
If we're just talking about Aztec cities, Yautepec offers three different kinds of homes (Smith et al. 1999). There are ground-level homes consisting of a double-row foundation wall, homes that have low platforms, and palaces. The double-row foundation homes would have had two rows of stones laid side by side with an approximate width of 60 cm. Build upon the double-row of stones was likely adobe bricks made in wooden molds. The floors of these homes likely consisted of just packed earth.
The platform homes consisted of stone platforms of a modest height of 40 cm to elevate the buildings above the ground. Unfortunately modern plowing stripped away any evidence of what the homes may have been like on top of the platform. Though enough evidence did survive to suggest that these homes may have had plastered floors.
Calixtlahuaca offers a similar example in home construction within the Triple Alliance (Smith et al. 2013). Many homes had double row stone foundations topped with adobe brick or sometimes wattle-and-daub.
If we stay in Central Mexico, but go back a little further in time, Teotihuacan offers another perspective on house construction (Murakami 2010). Teotihuacan was another large urban center built on a grid and consisting of apartment compounds where multiple families (sometimes even unrelated) lived together. These apartment compounds were constructed with shaped rocks bonded together using a mud mortar. The walls were then covered in a type of concrete or clay and lime plaster. The remains of roofs were covered in situ at Atetelco and the Quetzalpapalotl Palace. From these fragments archaeologists have been able to reconstruct how the roofs were built. Primary beams were placed on top of the walls that would have spanned from either end. Between these primary beams smaller wooden poles about 7 cm in diameter were laid across. Then the same type of concrete or clay/lime mixture was plastered on top of the wooden roof to seal it and help waterproof it. This would have given the apartments at Teotihuacan flat roofs rather than peaked roofs from thatch covered homes found in places like the Yucatan.
Murakami, Tatsuya. Power relations and urban landscape formation: A study of construction labor and resources at Teotihuacan. Arizona State University, 2010.
Smith, Michael E., Cynthia Heath-Smith, and Lisa Montiel. "Excavations of Aztec urban houses at Yautepec, Mexico." Latin American Antiquity 10, no. 2 (1999): 133-150.
Smith, Michael E., Aleksander Borejsza, Angela Huster, Charles D. Frederick, Isabel Rodríguez López, and Cynthia Heath-Smith. "Aztec period houses and terraces at Calixtlahuaca: the changing morphology of a Mesoamerican hilltop urban center." Journal of Field Archaeology 38, no. 3 (2013): 227-243.