It really depends on which nation you're talking about, as they had different resources to make instruments with, different aesthetic preferences, and contact with different other nations.

In Alaska, the annual Alaska Federation of Natives conference has a pretty good day of dance and music, and here's a poor-quality video from the state video archives from this year's event.

Alaska Native music is built around voice and drumming (if I were to make a generalization), and so smaller exhibitions (like this one from the National Museum of the American Indian) don't give you the full experience. You need to be there in person to feel the bass from the drum.

Dancing is an integral part of the performance, so it's not just aural -- it's also visual and physical. You need to move to the music to be part of it.

There's a lot of video on YouTube, so take a look for things from the Alaska Federation of Natives conference and Celebration, which takes place every other year in Southeast Alaska. That happened just this summer, so a search for "Celebration 2014 Juneau" should bring up plenty of results.

You've asked for traditional music, but I do want to point out that Native culture -- like any other active, living thing -- is constantly growing and changing. It's not static. Pamyua, for example, is a fun example of modern Native music in Alaska. They do a lot of good work traveling around the state and teaching kids, so I like to give them credit for what they do.

There are several groups that aim to perform traditional Mesoamerican music as has been filtered down through the ages while also aiming to re-create how the music originally would have sounded. As with the groups /u/The_Alaskan wrote about, dancing was an integral part of the music, with the copper bells and shell shakers worn by the dancers as part of the music. You can see how that works in this video of one of the re-creationist groups, where the guy on the left is integrating the rattle on his leg.

The truth though, is that our picture of what the compositions sounded like is not very clear. We certainly know that the music was heavy on drums, whistles/flutes, rattles/bells, and conch horns along with the singing of the dancers. Two styles of drums are prominent among the Aztecs in particular, the huehuetl and teponaztli. We have innumerable references to these instruments being played, but typically no more than "the drums, flutes, and horns were played in celebration/for a festival/during war." Putting the instruments together into an authentic composition where no records have been kept of the actual music is difficult. It's like having all the ingredients for a meal, but none of the recipes.

Here's a passage from Sahagún's General History of the Things of New Spain which gives you an idea of the kind of textual evidence we are working with, translated from a rather formal and roundabout poetical Nahuatl style:

And only in the calpulcos were those who beat the drum for [the procession]. They were only seated. They beat only the upright drums; they sat rattling gourd rattles; they sat erecting gourd rattles; they beat turtle shells; they struck turtle shells; they sat using turtle shells.

That is... not very helpful in distinguishing what exactly was being played. Both (2007) does a great job of marshaling textual and pictorial evidence to give some insight into the specifics of the actual music. For instance, he notes the Spanish called what he terms "Temple Music" things like "gloomy" and "dark," which of course may be the Spanish reaction to the context more than the music. He does though, go through how certain combinations of instruments were specifically played for certain festivals and that certain deities even had instruments associated with them, like the rain god Tlaloc being associated with rattles and clatterers mimicking the sound of falling rain.