Go and wander round the Madinat and have a coffee/meal overlooking the canals and the Burj AL Arab.
In the old town....Visit the Dubai Museum (the big bus tour drops off there) and wander round the souks, taking a boat across the creek, visit the traditional houses in Al Bastakiya and drop in at the Sheik Mohammed Centre for cultural understanding.
If there is racing on spend an evening at the Meydan racecourse.
Drive out into the desert/go on a desert safari
Go to the beach!!
Visit one of the 5 star hotels and gawp at the bling- many sell day passes for the pool etc.
Go to the waterpark at Atlantis or Wild Wadi
Go skiing at Mall of the Emirates
Go to Karama and buy genuine fakey, fakey handbags and watches
Take the guided visit to the Jumeirah Mosque - really informative and free
Take in a film - the cinemas are all fab if a little chilly.
Persuade DH to take you to the Gold and Diamond Park on Sheik Zayed Rd near Mall of the Emirates - every woman should leave Dubai with more gold/diamonds than she went with!!!!!!!
The weather should be good - not too hot.