Malls are generally open until midnight on weekends (Thu, Fri) and 10pm midweek, restaurants until midnight, bars until 2am, fast food all night in gas stations.

http://www.timeoutabudhabi.com for restaurants, etc
http://thecapitallist.ae for bars, music and clubs

Of course it'll be dark but the city looks good lit up and the grand mosque is spectacular if you ask the taxi driver for a drive by and photo stop.