On the campus of the University of Arizona in Tucson sits the largest and oldest anthropology museum in the SW United States. If the history and culture of the region interest you, this is the place--the museum is an affiliate of the Smithsonian and possesses the world's largest collection of Southwest American Indian pottery and basketry--the oldest object in their collection dates back to about 50 A.D.
A short walk away is the Main Gate area--a pedestrian shopping district that caters to the University's 40-thousand or so students; plenty of restaurants and pubs for all budgets...
(The particular piece in the photo above shows the traditional Tohono O'odham method of harvesting saguaro-fruit--using a long crook and head-strap back-basket.)
The "Native Goods" gift shop is well worth a look; the museum is closed on Mondays.