I was only in Dubai for a couple of days but they have made a metropolis out of the desert!!! The TV adds are true, it is amazing for browsing and shopping. There is everything you could imagine in all the designer stores you could possibly think of, I forget the name of the large shopping center I went to but just ask a cab driver to go to a large mall and you should get there quite easily.
Even if you're "just looking" (lol) you will be amazed with the MASSIVE fishtank aquarium that has been built into the wall as well as the waterfall near the center of the mall. I've never seen that many sports cars inside a shopping complex before but it was pretty cool to see the expensive names on display.
Look around and you will also find the indoor waterparks and snowfields, absolute AWESOMENESS for a day of fun!!! Amazing to see what they have built in that devastating desert heat!!!!
If you're looking for a definitive shopping experience than Dubai is it, but if you're on a budget, steer well clear!!!!