The best place to buy native american art or other characteristic types of durable mementos is in the near by town of Mesilla. If you want something to remember your visit by, one idea is food, specifically chile peppers, which are grown in abundance in the Mesilla Valley. The long strings of red chiles that you see hanging from porches, gables, etc., are called ristras and are available for purchase at many locations. These are largely for ornamental purposes, but edible chiles are also widely available, with spiciness levels ranging from mild to downright inedible New Mexico State University has a substantial chile research program that grows peppers so hot that they function as bug repellents.
If in town in late summer or fall, make a pilgrimage to the outlying town of Hatch on I-25 to the north. Hatch is the center of the chile-growing business and has several shops with chile paraphernalia. Better, it hosts a "Chile Festival" in early September, usually around Labor Day, that's fun to visit as well as a great source of chiles. Hatch is a tiny town with little or no lodging, so you'll want to stay in Las Cruces and make a day trip to the Festival. If you're getting your chiles for cooking rather than ornamentation, and can get them home/in a freezer quickly, get them roasted while you're there; roasting is a key step in preparation for the table, and doing it in a Hatch roaster will save you all manner of peculiar odors resulting from doing the roasting at home.
For more pedestrian, day-to-day purchases, Las Cruces has all of the usual shopping associated with a town of 80,000. Mesilla Valley Mall is convenient off I-25 just north of NMSU for this purpose.
