I can think of one...haha...the Dubains amongst us will probably flame me for this because they see it everyday....but there is the Burj al Arab. I hear it's nice on the inside but never went...I aint paying to get into a hotel then have to pay $50 for a cup of tea!
Hehe. I bought a good book on my birthday called "Time Out - Dubai, Abu Dhabi and the UAE" It's got the sails from the Dubai Creek Golf Club on the front...I swear by it when I'm in Dubai.
They do a little section in it called "Customs and Exercise" which is a walking tour of Dubai...now if only I had the book in Scotland with me (left it in Dubai...) then I could tell you about it!
If you're interested in the cultural side of things then the Jumeirah Mosque gives tours to non-Muslims every Sunday and Thursday at 10am. See
www.cultures.ae for more information.
There's also Al-Fahidi fort which is home to Dubai Museum.
Both of these I've never visited but will do next time I'm over.
I'll just say one more place...Wild Wadi. It's a great waterpark but make sure you spend the whole day there to get your money's worth...the AED165 entrance fee can prove steep if you only plan to stay for 2-3 hours!
Hope this helps.
Ross