New Dubai Sights

Burj Khalifa ( map | official site ), currently the tallest building in the world, is located next to Dubai Mall. I recommend going just before sunset (maybe around 5 pm) so you can see the view in the daylight, the sunset, as well as the night view. Costs AED 125 for adults. Of course, don't miss the New Year's Fireworks!
Burj Al Arab ( map | official site ), the 7-star sailoat hotel, is not open for non-guests. You must have a reservation at one of its restaurants to be allowed to cross the bridge onto the man made island it resides on. 395 AED gets you afternoon tea at Skyview Bar with champagne and snacks. The food was not the best but the view was absolutely breathtaking.
The Walk, Jumeirah Beach Residences
( map | official site ), is a beachfront promenade lined with apartments, hotels, restaurants, and nice cafes. It's a great way to spend an afternoon, chillaxing at a cafe then walking along the beautiful Jumeirah Beach.
Join a Desert Safari, which is a day trip consisting of dune bashing in the desert, camel riding, sand boarding, followed by performances of whirling dervish and belly dancing during dinner. There are many tour operators and prices to choose from.
Atlantis the Palm ( map | official site ) is a man-made palm-shaped island with some fancy condos and a hotel at the end, in addition to a mall and a water park. You can get there via monorail or taxi. Check out the Lost Chambers Aquarium, a cool little aquarium with an Atlantis theme. The quiet, mysterious atmosphere sets it apart from other aquariums.
Wild Wadi Water Park ( map | official site ), a fun water park with an amazing view of Burj Al Arab and the beach!

10 am - 6 pm

AED 275 for adults
AED 175 for children under 110 cm
Check out the beach ( map ), a short walk from the Jumeirah Mosque.
Emirates Towers ( map ) are 2 towers with office space and hotel rooms. Cool buildings but not much to see here really.
The Dolphinarium, located inside Creekside Park ( map ), has a pretty depressing dolphin show with some probably Russian acrobats. I felt horrible for paying for this.