I used to live in the UAE and would heartily recommend Dubai for a visit. It is a fantastic city that has grown tremendously since the early Seventies. The gold souk is superb, as are most of the souks, but remember to haggle. The Creek is worth a jaunt and the rugby club at the weekend is well worth a visit too, but there is so much to see and do. Hili Fun City near Al Ain is a good day out, as is Al Ain, the garden city of the UAE, and the nearby Jebel moutains. Abu Dhabi is just over an hour from Dubai and much less humid. From Dubai you could visit Sharjah and it's famous souk, try wadi bashing, go out with the Hash House Harriers or just relax by some of the most beautiful beaches.
Weather is hot and humid, but winter sees a temperature drop. Do not go in the summer unless you can stand very strong tempreatures, usually in the high forties.