Depends on how late you land, I had about the same amount of layover like you 8 months ago. I went outside to see the city, as soon as you step outside the airport, you will see a bunch of workers mostly immigrants stepping out and getting on the bus. There are public buses right outside the airport, I think I paid about 20 bucks and you get all day pass. The bus is mostly empty so it's like getting a taxi. Most of the bus drivers I saw were Africans.
Ok so if you get there around 6/7pm go to old bazaar, its about 20/30 mins from the airport on bus. The bus will drop you off in front of the parliament building, you can see the ocean view and walk on the boardwalk, you can also see the skyline of Abu Dhabi from there pretty good view. You have to cross the street to go to the bazaar, its an old market kinda like asan of kathmandu but really cool, pretty much every Arab country has one, you can try some kebabs, they got the ice cream stands like Turkey that do tricks and a lot of small shops to buy some souvenirs and you can bargain like Nepal.
After that you can tell the driver to drop you off at the mall, the malls are alright, nothing spectacular. I just went to the starbucks, drank some coffee and used the free wifi. That was it for me, may be you can do more and have more fun.

Thank you for your advice. I will keep them in mind. I arrive a bit late 9:30 PM so hopefully those places are still open.