Took a tour, arranged with the Hotel around Dubai. It was great to see the contrast between old and new. It was also extremely helpful in orientating you to the city itself. I recommend you do this within a day of arriving.
Also, Gold Souk. A block full of Jewelery stores. Be prepared to spend money, be prepared to haggle (not as tough as it seems). The gold is excellent standard and excellent value.
Fake Stuff. It's intersting to note that no fake brands are on sale in the main parts of the shops. You have to ask for it and you will be brought upstairs to an Aladdin's cave of merchandise.
Quick Tips:
If you wear glasses, they will fog up when you step outside. The same thing will happen to Cameras and Cam-Corders.
Bring water with you. When we were there it hit 45 Farenheit and over 100% humidity.
Go shopping at night. Everywhere stays open until 22:00. Spend the afternoon by the pool.
Best Way To Get Around:
Taxis are plentiful and cheap. However Dubai is growing all the time, so a couple of times our taxi driver didn't know where our hotel was, as it was only newly opened. Be prepared to tell the driver other hotels near your one as a a way of going in the right direction.