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Eat, sleep and hunt for Aurora Borealis! That is more or less all you will have time for, because during the day you will exhaust your self from running around different sites.
As far as Aurora do not book any tours they are waste of money. All you need a decent DSLR, rent a car and to check these three sites and you will be set.
Here you can search for open patches of clear sky: http://en.vedur.is/weather/forecasts/aurora/
Here you can find locations without light pollution (more or less entire island of Iceland minus (Reykjavik area) : http://darksitefinder.com/map/
Aurora cloud map: https://play.google.com/store/apps/details?id=eu.dziadosz.aurora&hl=en
P.S. Don't get discouraged with low KP or probability factor. We saw Aurora 5 nights in the row and have hundreds of pictures even though KP did not go over 3.6 and probability was never more than 34%
As far as night life, we didn't really find anything interesting during our stay in Reykjavik ( 3 nights in total )
There is bunch of bars around that main street but almost all of them were empty even during happy hour.