ALERT: This is a different operation from the Arizona Historical Society Museum a block or so away.
First of all, don't set your expectations for the size of the museum by what you see from the outside, since the museum actually occupies only the first floor of that big building on the University of Arizona campus. However, that small space is well used for interesting cultural exhibits. When I visited, there was a very informative exhibit on the history and culture of Mexico that included representative artifacts from pre-Columbian times, as well as Santa Anna's ceremonial uniform. The exhibit on the Native American cultures of the area was particularly informative in conveying much information without generally resorting to those small text boxes that hardly anyone ever reads. (I have a friend who is a museum director, and she tells me that this is common knowledge in the profession.) There was also an exhibit of Hopi quilts, and a large permanent collection of pueblo pottery and basketry stretching from a few thousand years into the past to modern works by top artists.
To net it out: This may not be your first stop on a tour of Tucson, but, particularly if you happen to be on the UA campus, it is worth the small admission fee to see what is there.
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