The Alhambra is a Moorish citadel, a group of buildings on a hill overlooking Granada, Spain, built between 1230 and 1354 that formed a great citadel of the Moorish kings of Spain.
In regard to the South Bend allusion, Myers recalls one large movie palace that no doubt dated from the 1920s, but "I simply don't remember either its name or decor, despite having seen dozens of movies there over the course of four years. That was the era when theaters with outlandish, exotic decor were being built all over the country. I'm guessing that Bellairs inadvertently conflated the two names and mis-remembered the true name of the theater in South Bend."
Where they have been a handful of theaters in the United States that carried this name, none were located in Indiana.