Alexandria isn't a shopping city. There's little to buy here that you can't do better finding in Cairo, where the selection is much greater. If you're looking for chain stores, try Shar'a Suriya in Roushdi, Alexandria's most upscale neighborhood (15 minutes east of Downtown by taxi), or one of the new shopping malls that have opened up in the past few years.
Downtown has a large number of shoe stores, but most of the shoes are of poor quality. The best are on Falaki Street (try the Armenian-owned Gregoire or Fortis), where, given enough time, the chaussuriers can produce custom-made shoes at a fraction of the price they would be in Europe or the United States.