I agree with Jamoldo, 6 hours is really cutting it close. DXB is large, and immigration can take a long time -- it usually takes me a good hour to get out, plus you should allow two hours to get back in.

So that leaves three hours. You could do any number of things:

(1) Have a taxi drive you along Shaikh Zayed Road along a loop to the Mall of the Emirates (on your left), then to the Marina (on your right), then along Jumeirah Beach back toward the airport. With no traffic, this trip would probably take 1.5-2 hours, and you'd see the basic skyline and key landmarks in the city. But, as I am sure you have read about Dubai, "no traffic" is unheard of and the traffic on these main routes can be horrible. Frankly, I would not risk this with three hours.

(2) Take a ride to Deira, the old part of the city, and walk around downtown and the creek. This is not too interesting, but you could do it 3 hours -- with no traffic, it could be as little as ten minutes each way, but allowing 30-45 is more realistic.

(3) Just relax and have a meal somewhere near the airport, like the Park Hyatt, Sheraton Dubai Creek, or Le Meridien.