My advice (assuming that you actually want to go to Dubai – I would take CFH’s advice):
Watch the sun set at the 360 bar.
Watch the British expats at Barasti beach bar.
If it’s warm go to either the Wild Wadi or the Atlantis water parks.
Check out the aquariums at the Dubai Mall or the Atlantis Hotel. In either case I probably wouldn’t pay to go in just enjoy from the public areas.
Go to Bur Dubai, it’s great, very lively. Eat the shawarmas, visit the souks, take it all in.
If you’re looking for an upmarket meal I can recommend Teatro restaurant in the Towers Rotana hotel.
You can cross the creek on RTA dhows (much cheaper than going on a dhow trip).
Possibly a desert safari?
If you want to mountain bike contact the Hot Cogs.
Edd