So most of the interesting stuff has been mentioned. But I think I would emphasise the following:
Dubai Mall. Huge, impressive, definitely check out the ski slope, it’s like no other indoor ski slope I’ve ever seen. Even if you don’t ski or board go and grab a drink in the restaurant with the chalet style balcony overlooking it all.
Deira Spice and Gold Souk. This is great, get on the water taxi boat with loads of other people, get shouted at for payment (it’s not much but make sure you have the cash) walk around the Souk and get hassled to buy weird spices and jewellery – it sounds awful but it’s quite fascinating if you can avoid being annoyed by the hassle.
Burj Khalifa. Go up the elevator to the viewing platform (125th floor), look out at not much, go back down again and then watch the fountain show.
Show at the opera house could be worth it if there’s anything decent on.
Wolfi’s bike shop is pretty cool for a visit, some fancy bikes.
Atlantis for the aquarium and waterpark.