To explore at least few Dubai shopping malls (typically accommodating hundreds of shops, not to mention restaurants and entertainment) you have to be some kind of a god of trade, not a mortal human being. If you just want to know what Dubai shopping is like, simply choose one grand mall. How do you choose one? Dubai shopping malls vary by the entertainment they provide.
For authentic souvenirs go to traditional markets (“souks” or “souqs” in Arabic).