We stayed at Kempinsky Hotel, and although, not close to the airport, it proved to be a marvelous choice. First, the hotel is attached to the Mall Of Emirates and SkiDubai, so if you want to shop or ski, it's most convenient. There are also many inexpensive choices to eat at the hotel and nearby. The concierge at Kempinsky is second to none. They arranged for us the most incredible/fun desert Safari we have ever taken. The driver was amazing. He played American Rock and Roll while we were going up and down the sand dunes: quite surreal! Thirdly, the hotel is included in the stopover for Dubai BUS tours; the pick up is right outside. If you don't know, the bus tour is a double decker, 2 routes, and you can get on/get off as you wish; I definitely recommend it;
Finally, we had prearranged transfers via bus from airport to hotel by Emirates Airlines. It was definitely worth it; On the way from airport to hotel we hit rush traffic which was cool becuase we got to savour some of the city views and take pictures (and not have to worry about paying cab fare); on the return to the airport we were picked up at 5 am by a limo (nice little touch by Emirates).
Good luck