1- Dubai creek and the Abraa (Water taxi). A very unique experience that changes from the modernism of the city. This mainly consist of doing a tour of the creek on a small boat.
2- The Gold souk: a very authentic and unique experience!
3- Desert Safari: Even though this attraction can seem to be very touristic it is still very interesting and fun! It is also a cheap way to do a tour in the desert and have a barbecue there. I wouldn't advise to do sand surfing as it is difficult and not fun for beginners.
4- Dubai creek (golf and yacht club): where you can have a drink while looking at an amazing panoramic view.
5- Bab el shams: a more expensive experience then the rest. But this hotel situated in the middle of the desert is a wonderful place to have diner or to spend a week end. You can also enjoy the spa! If you decide to go there, try to arrive before the sunset as it is a unique experience to discover!
6- The Dubai Mall: Shopping in the biggest mall on earth can be quite amusing since they have one of the biggest aquariums in the world!
7- Ski Dubai: The world famous ski slope! If you are a huge ski fan, skying there won't give the best sensations of your life. The slope is quite small but it is fascinating to see in the middle of the summer!
8- Atlantis: The brand new hotel of Dubai. It is very impressive to go and see this huge resort. It has a very big aquarium, an aquaventure park and a dolphin attraction. The water park is worth it if you have a day to spend there.
9- Dubai Museum, Al bastakiya and a tour in bur Dubai: The less sexy of all attractions but maybe one of the most interesting. You can discover Dubai under a new face. This will take you through the small old street of the city. The museum is very interesting and shows how Dubai went from a desert to what it is today. Here are two picture to illustrate the difference between this area and other parts of the city:
10- Souk al bahar: Situated in the old town next to burj Dubai, this souk is perfect to have a walk and a coffee while looking at what will be the tallest tower in the world. Even though it can be tempting, prices are very expensive and you can always find the same things (or similar) cheaper in another souk or mall.