If I had said I went to “the mall in San Antonio,” it would be implying that there is only one mall in San Antonio, which may or may not be true. At least that’s the way it sounds to my ears. YMMV.
Yes, I suppose I could say “I went to a mall to buy shoes,” but, again to my ears, that would make it sound like the story was more about the mall I went to than about the shoe-buying experience. It would be like saying “I went to some mall” almost as if it were a random mall I was not familiar with. However, saying I went to “the mall” or “the store” implies it was just a routine trip. Even if it were a mall or store I had never been to, the story I’m telling is about what I bought, whom I saw, what I did there, or whatever. The particular mall or store has no bearing on the story.