Cairo has always been a great place to shop for traditional items because of its spectacular medieval marketplace, the Khan al-Khalili, where browsing and bargaining are half the fun. There is no tried-and-true bargaining strategy; just shop around, decide how much something is worth to you, and start bargaining lower than that in order to end up at that point. In the Khan, the opening price is never the final price.
In the last decade Cairo has embraced the shopping mall. These enclosed, air-conditioned spaces stacked with international brands have revolutionized shopping for residents. Most malls also have shops selling a range of the same kinds of souvenirs that you'd find in the Khan al-Khalili, though at higher, nonnegotiable prices.
Wealthy and upwardly mobile Cairenes not only have the wherewithal to fund their lifestyles, but they also have great taste, so you'll find a wide selection of art galleries, designer shops, and fashion boutiques to indulge your need for retail therapy.
Although most of what you see in tourist shops are reproductions of varying quality, there is a long local tradition in Egypt of connoisseurship in collectibles, which means that there is always the possibility of finding a real gem. Be prepared, however, for local tastes that favor ornate French-style furniture and antiques, not the Middle Eastern pieces you might be longing for. There are several nameless antiques shops in Downtown Cairo along Shar'a Hoda Sharaawi that are worth looking into. Lots are shown for several days in advance of a two-day auction, which usually operates on a cash-only basis. Check the Egyptian Gazette for the latest auction schedules.