This lovely building is a small part of the Nogales Public Library in Nogales, Arizona. Cynthia makes a point of visiting local libraries when she travels, though she has not yet been here. She discovered the photo was taken in 1963 and the architect is Bennie Gonzales. This was one of his first buildings, and it won him an award from the American Institute of Architects.
Libraries are sometimes better than tourist information centers for visitors to find out what is going on in town. There's usually a community bulletin board with all sorts of events that could prove to be more interesting that official visitor center event listings.