Go to the texile souk to grab some cheap fabric. Remember to Bargain!
Go to the gold souk to grab some cheap gold jewelleries, used branded watches like IWC, Rolex etc.
Go to Dubai mall (proclaimed the largest mall in the world) to visit Tom Ford, Brioni, JM Weston, John Lobb, Canali, E. Zegna etc but mind you even it was stated as tax free state, doesn't mean the items that are cheaper than Europe or US.
Go to this resort, Madinat Jumeirah which is beside Burj a Arab, they have a very nice water canel just like Venice. hop on the Abra (Arabic style boat) and tour around the resort for $10. A lot of good restaurants over there too. Average spend about $150 per person. Smoke sheisha at the beach and have some nice cognac.
Go to the Dessert Safari. The whole package inclusive of the camel ride (at least photo taking), trying some arabic food, watching belly dancing in the tent and riding on the sand dunes.. Cost about $100 per person.
If you have money - try the hot balloon trip across the dessert. Think about $300 per person.