On the topic of the Aztecs, an intriguing book on this subject is Aztec Warfare: Imperial Expansion and Political Control, by Ross Hassig.
The Aztecs were an extremely war-like civilization, that were constantly attacking and subjugating their neighbors. Interestingly, though, their style of warfare was quite different from what we are familiar with from western european history.
For the Aztecs it was all about taking prisoners. The more prisoners you could bring home to sacrifice to the gods, the higher your standing. Thus, weaponry, tactics, and military strategy were all geared around maximizing capture of the enemy rather than defeating them in detail. They didn't really care about securing administrative control over their conquests quite the way the Europeans did, and often allowed the conquered to continue under their existing leadership, so long as they continued to send tribute.
Typically the Aztec army would set forth from the capital at the start of the war season and go from one town to the next. They might start with towns that were lax in their tribute or that had refused to give it. When they appeared at a town, those people had the choice of surrendering or going to war; the Aztecs would be particularly harsh to those that resisted to dissuade others from doing the same.
Flower War was another interesting warfare technique rather unique from European war; the nobility would leave their regular troops and engage in non-lethal battle with nobility of neighboring empires. These did not result in capitulation of their enemy, but were done for practice, honor, and to "test" the strength of the opponents. I suppose there is some analogy to the jousting tournaments of the European middle ages.
Thus the Aztec empire was always a bit amorphous, with cities and towns shifting in allegiance depending on the strength of the king, the proximity of the army, and heaviness of tribute demands. The empire was maintained not by territorial control via castles and forts, but rather indirectly via political influence, propaganda, and fear. It also meant that the maximum effective range of the Aztec empire was limited to how far the army could march in one war season.
Thus, while the Aztecs probably would have no qualms about conquering, say, Texas, the structure of their civilization would just not support such a long range expedition.
Also, the central Mexico basin was a very agriculturally rich area and supported very large populations. Outside this area populations were more scarce. So I think the Aztecs would not be as interested in areas far from them where captives would be harder to obtain and more time consuming to bring back for sacrifice.
While the Aztecs were distinctive compared with Europe, they didn't live in a cultural vacuum. Neighboring empires followed similar style warfare, prisoner capture, flower war, and so on. Religious practices, agricultural technology, war strategy, and more would drift northward, influencing the practices of other Native American tribes. The Flower Wars remind me much of the "counting coup" of the plains indians for instance.
For contrast, I'd suggest reading Empire of the Inca by Burr Cartwright Brundage.
The Incas engaged in war for keeps. They didn't take captives for sacrifice, they wanted territory. When they took a new region, they'd transfer some loyal families from Cuzco to serve as the conquered region's ruling class. Dissidents would be rounded up and relocated elsewhere in the empire. The Incas would terrorize the newly acquired until they accepted the Emperor's law without question.
They also practiced warfare in a much different fashion. War was not to win social standing but to take territory, so their armies were organized much more differently; as they often faced enemies fortified in cliff-high strongholds they developed "tortoise" shield-rush tactics that would have impressed the Romans.
Logistics were the Inca's particular talent. While marching within the borders of their empire, they would enlist the commoners of the province as porters to carry goods from one end of the province to the next, whereapon they'd hand off to people of the next province. The people would open up their granaries to supply the marching army; foraging and looting were strictly forbidden.
The Incas also had a unique ability to "snowball" as they took new lands. Upon taking a new province they immediately enlisted the military man power of that province into their army, to be used as the cannon fodder for their next campaign. This both strengthened their army and depleted the resistance power of the new province.