Lived there for three years. Desert dinner at Bab Al Shams, I would say is a must do. They have a dinner show with belly dancers (tasteful) and riders on horseback that have a short fight scene with swords that is pretty cool. Food is really good too (Arabic Barbecue). It's about 30 minutes into the desert, but if time allows, you might consider staying there for 2-nights, enjoying their beautiful pools and going to the desert dinner in the evening. Ski Dubai is pretty cool to see at Mall of the Emirates also.
https://www.babalshams.com/Burj Al Arab - (You'd need to dress-up) but the Sky Bar at Burj Al Arab is a great reservation and way to get inside the Burj Al Arab without having to pay $2K+ per night to stay there. It's a beautiful place.