At first - Reykjavik's entertainment. All the bars, restaurants, clubs and so on are closed at 1 A.M. on weekdays (despite the fact that the amount of tourists raises every year). So you won't find A SINGLE working place at night (if you find, please tell me). Sometimes you may be lucky to see bars, that are open till 3 A.M. By the way, local bars are veery atmospheric, and it often comes with Icelandic live music, which I can say for sure is the thing they make professionally.