1066 is an interesting time in Mesoamerica, coming as it is during the early Postclassic or (depending on how you want to look at chronology) the Epiclassic.

In the Maya regions to the South, the Classic Collapse saw the decline of most major sites in the lowlands of what is now Guatemala (particularly in the Peten region), with the population centers shifting northward in the Yucatan. By 1066, earlier Yucatan sites like Coba and Uxmal had been eclipsed by the growing dominance of Chichen Itza. The latter half of the 11th century, however, saw Chichen Itza starting on the downslide, with an increasing importance of Mayapan.

The transition from Chichen Itza to Mayapan as the most significant centers in the Yucatan is often seen as influence from Highland/Central Mexico receding and more "pure" Maya groups reasserting themselves. It's certainly true that Chichen Itza had clear links northward, particularly to the Toltecs, and that the conquest of Chichen Itza has a place in the founding legend of Mayapan, but it's important to realize that this also coincided with the decline of the Toltecs, which meant an overall decline in Central Mexican influence.

One thing we can certainly say was one the rise in the Yucatan was trade. Though it has roots in the Late Classic, circum-Yucatan trade in the Postclassic would become a major factor in the development of settlements and wealth.

Moving northward to the aforementioned Toltecs, at this time they were at their height, with their capital, Tula, having upwards of 60K direct inhabitants and more in the immediate surrounding areas. While the notion of a "Toltec Empire" is largely discredited now, it is undeniable that they were not only a dominant regional power, but also influenced other groups in the larger Mesoamerican sphere (most notably Chichen Itza). The Toltecs were particulary influential over the polities in Basin of Mexico, both militarily and through alliances. One of the latter, with Culhuacan in the southern basin, is particularly important, as it would be seen as an heir to the Toltecs later in the Postclassic and marriage into its ruling dynasty would give legitimacy to the Mexica.

Heading just a bit South, during this time the ancient city of Cholula was in an ebb period, following the tumult of the Epiclassic, but was not yet in resurging to become the major center it would be in the later Postclassic.

Heading to Southwest to the Valley of Oaxaca, the previously dominant Monte Alban likewise did not survive the Epiclassic. By 1066, the previously flourishing city had largely been abandoned and Oaxaca was broken into competing Mixtec and Zapotec polities like Mitla, Zaachila, and Jalieza. Of note at this point is the city of Tilantongo, where at this time the famous Eight Deer was just a baby. As an adult, and ruler of the city, he would conquer large swathes of Oaxaca, before being defeated and sacrificed.

Moving North from the Valley of Oaxaca into West Mexico, this was a very interesting time. The older Teuchitlan tradition has ended, replaced by the Aztatlan style. We also see the flourishing trade running up West Mexico between Mesoamerica and what is now the American Southwest, leading to things like ball courts and macaw feathers showing up in among the Pueblo.

Over on the Gulf Coast, El Tajin was dominated the region. It too would soon decline as the migrations which brought about the end of the Epiclassic/Early Postclassic proceeded. Within roughly a century it would decline, leaving the coast controlled by feuding Totonac polities which would be swept up by the Aztecs.

That's just scratching the surface of some of the major regions, but should give you a gist of what was going on at the time. Evan's Ancient Mexico and Central America: Archaeology and Culture formed the backbone of this, but I also consulted Coe's Mexico: From the Olmecs to the Aztecs, Davies' The Toltecs: Until the Fall of Tula, and Sharer and Traxler's The Ancient Maya.