About a month ago I had a short transfer in the United Arab Emirates on my way to Sri Lanka and Australia.
Although I landed in Sharjah and not Dubai I decided to see Dubai during my transfer. From the Sharjah airport I took a small bus for 10 AED (less than 3 USD) that goes to Lamcy Plaza in Dubai.
The bus trip took one hour and after arriving I walked for about 30 minutes to get to the nearest metro stop which I randomly found, trying to walk into the center. If you are not into walking you can also find cheap taxis waiting outside Lamcy Plaza. Read about other hotels in Dubai (in Swedish).
I can highly recommend to take longer transit times when flying, which will allow you to explore a “bonus destination” without paying for an extra flight ticket. Just remember when you go away from the airport to check the possibilities for getting back to the airport again in time for your next flight.