On your 1st day, explore the Dubai city. Go around Mall of Dubai, the largest mall in the world. Check out Dubai Aquarium in the mall and other fun activities if you wish to. Dubai Mall is huge and one can easily spend an entire day in the mall.
If you fancy, adventure parks, visit IMG World of Adventures. It is an excellent adventure mark that has theme rides.
On your 3rd day, you can go for a Dubai Desert Safari. It is indeed one of the best activities to do in Dubai. Have a fun safari ride in the desert and then enjoy your evening having a desert dinner.
On your 4th day, you may want to visit Jabel Hafeet, the highest peak in the UAE. It gives a significant sunrise or sunset view. In the evening, you can stroll around Dubai Marina.