It really depends what kind of activities you're into. In terms of outdoor stuff I would recommend a desert safari of course. If you have more than just a few days, you could even book an overnight package for that.
Then you can go Jetskiing at Mamzar Park, drive around the Dubai Autodrome, visit Wild Wadi and the beaches, go for a skydive at UAQ Aeroclub, chill out at the Le Meridien Mina Seyahi, etc.
That's all I can think of at the moment. If you are travelling in the next few weeks, the weather will be very nice. You might experience a few rainy days in December though.
Umer, are there any tour groups that offer these packages? or do you suggest exploring on your own is better? Thanks.
All other dubai guppies, can you kindly suggest a reasonable place to stay? many thanks!