There are ethnographic accounts (No sources for now, just from in-class discussion with my Art History/Mayanist/Olmecista professor) of the Aztecs being appalled by the hygiene of the incoming Spanish. This may be due to the fact that they were solider/explorer/15th century "religious roughnecks", but European culture of the time didn't place an emphasis on staying clean (in fact preferring the opposite).

The late epidemiologist Velvl Greene discussed European hygienic practices:

“The fathers of the early church equated bodily cleanliness with the luxuries, materialism, paganism and what’s been called ‘the monstrous sensualities’ of Rome..."

"Cleanliness wasn’t a part of the folk culture."

"Within a few centuries, the public and private sanitation practices of Greece and Rome were forgotten; or, as Greene adds, were “deliberately repressed.”

Additionally, Spanish Queen Isabel of Castille famously (and proudly) claimed to have bathed twice: at birth and marriage.

For the Aztecs: from David Carrasco's Daily Life of the Aztecs:

"We can imagine, given all this emphasis on decorum, proper behavior, and guided training, that Aztec peoples valued clean, neat, and attractive personal appearance... Aztec peoples enjoyed bathing and personal cleanliness, and they used the fruit of a soap tree and the roots of certain plants for soap. They took cold baths but were especially committed to steambaths. Many homes had steam bathhouses, some of which have been excavated in the Basin of Mexico. These steambaths were used for ritual purification, during sicknesses, and to help pregnant wome, but also as part of daily hygiene."

From Manuel Aguilar-Moreno's Handbook to Life in the Aztec World:

"Cleanliness was one of the most cherished virtues of Aztec society for all citizens, not just women...Most people bathed often, and some bathed everyday."

I have to go to class, but I'll expand from there later.

What about Venice? Since it was equally as "watery" as Tenochtitlan.

In addition to the ubiquitous temazcalli and emphasis on bathing (Motecuhzoma II was said to bathe twice a day) the emphasis on personal cleanliness most certainly extended out to the city. As /u/Ahhuatl alludes, there were workers employed daily to keep the streets clean, but my favorite example of the integrated hygiene practices of the Aztecs has to do with their poop. There were public latrines along the canals and causeways, whose bounty would then be collected via canoe to be used for tanning and fertilizer.

Harvey (1981) is a classic overview on the subject. It also includes a quote from the Historia General on personal cleanliness which comes up in just about any discussion of the subject:

And when already thou art to eat, thou art to wash thy hands, to wash thy face, to wash thy mouth .... And when the eating is over ... thou art to pick up (fallen scraps), thou art to sweep the place where there has been eating. And thou, when thou hast eaten, once again art thou to wash thy hands, to wash thy mouth, to cleanse thy teeth.