The answer is, yes, the Aztecs did have maps, the Oztoticpac land map springs to mind. This 'map' is actually a land survey showing the holdings of lords and townships in the Acolhua region of the Valley of Mexico. The map itself was written/drawn in Native style and on indigenous paper. However, it is essential to note that it was actually produced during the Colonial era (According to Howard Cline in about 1540), and contains a series of notations in both Spanish and Nahuatl, probably for use in court.

There is also the Maguey Plan, which may come from either Tenochtitlan or Azcapotzalco. Again, this document is a land survey intending to show the locations of fields, canals, and causeways in the chinampas region of the Valley of Mexico. Other rural townships were also known to retain extensive maps of land holdings, which they used in court to protect their territory from outsiders (either Spanish or rival Indigenous communities). However, few of these documents were originals, which were lost, destroyed, or hidden, and so copies were used. It was not uncommon for these copies to be doctored, or even forged to bolster a townships claim to land.

So, for Mesoamerica at least, maps were a thing. However, they seem to have been mainly in the form of land surveys, rather than geographical. However, this may be due to selection bias. Land surveys may have been preserved (in rural zones), while other maps were destroyed when urban libraries were put to the torch during colonial battles.

Sources: Calnek, Edward E.: ‘The Localization of the Sixteenth Century Map Called the Maguey Plan’, American Antiquity, 38/2 (1973)

Cline, Howard F.: ‘The Oztoticpac Lands Map of Texcoco 1540’, The Quarterly Journal of the Library of Congress, 23/2 (1966)