24 hr stop in Dubai

It depends on what interest you. Most certainly head to the Dubai Creek area. The souk (markets) are all here. While not typically traditional (like in Fez) they're fun. You won't see many Emiratis here. They all go to the mall. Be sure to take an Abra (water taxi) from one side to the other.

The Burj Khalifa is the tallest building in the world. Tickets cost 100AED (about $30) Since you are short on time, it might be a good idea to book on-line

The famous Burj al-Arab (the hotel) is kind of isolated. There are buses that go nearby, but a taxi might be better with your time restraints.

Great!!! some of the places you can visit :

Deira Gold souq - a shopping destination for gold and silver jewellery
Dubai Mall - one of the biggest shopping mall with aquarium
Burj Khalifa Tower - Tallest tower, one of the latest landmark
Burj al arab - 7 star hotel located at jumeira beach
Mall of the emirates - Shopping mall with Ski (also called skidubai)
Atlantis Palm Jumeira - famous hotel to have fun with water, dolphin
Dubai museum and heritage: local heritage and cultural place to get some insight on the history of dubai

Tours : Bigbustours (will take a round on dubai covering major mustsee places)
Desert safari : a fun, thrilling, tour overnight stay in the desert. Music, dance, cultural, camerl ride, belly dancing, nice buffet (its hot nowadays, but get slightly cooler in the night in the desert)

You can use taxis, dubai metro to get to these places.

Enjoy!!!!

OP : there are a few threads on this subject in this forum which you may find useful if you do a search.

I used to tell people the big bus tour,but somebody who took it said you sit in traffic most of the time and they could have done better in a taxi.I say take the metro close to the place you want to go then take a taxi.