Istanbul's Grand Bazaar (Kapali Carsi, or Covered Market) is Turkey's largest covered market offering excellent shopping: beautiful Turkish carpets, glazed tiles and pottery, copper and brassware, apparel made of leather, cotton and wool, meerschaum pipes, alabaster bookends and ashtrays, and all sorts of other things.
Most guidebooks claim that it has 4000 shops. Because of consolidation and replacement of shops by restaurants and other services the number is certainly lower, but you get the idea: it has lots of shops. Not all of them, by the way, are for tourists; locals shop here as well, lending a welcome dose of authenticity.A dozen restaurants in the bazaar allow you to have lunch in the midst of your shopping. Note that the bazaar is closed entirely on Sunday, as is the Egyptian (Spice) Market. (These bazaars also usually close at mid-day on the day preceding major multi-day Islamic holidays, and stay closed for the holiday's first day, but then open on the second day of the holiday. More...)
You'll want to hone your bargaining skills before you plunge into the markets. Tips...
Beware of pickpockets and bag-slashers in the crowds.
Divan Yolu, the avenue from Sultanahmet to Beyazit Square (the large plaza next to the Grand Bazaar) offers many interesting sights so the walk is a pleasant one.
However, the easiest way to get from Sultanahmet to the Kapali Carsi (and vice-versa) is via the Zeytinburnu tram uphill from Sultanahmet; get out at the Carsikapi stop.
By the way, going by taxi is not so great (and certainly not cheap) because your taxi must negotiate a tortuous route around one-way streets, pedestrian-only and tramcar-only areas.
For funny stories about buying antiques in and around the Grand Bazaar, see my Bright Sun, Strong Tea excerpts entitled "Aladdin's Lamp Shop" and "Rockefeller Geldi!"