Copenhagen or Bust!

I am headed to Copenhagen in late August to research the civil-military dynamics of the Danish involvement in Afghanistan.  Denmark presents something of an anomaly as it has been quite active throughout Afghanistan and especially in dangerous places in the south (Helmand), unlike its Scandinavian and German neighbors.  For our work, it is also interesting that Denmark has had a coalition government, which we have tended to associate with countries with relatively tight restrictions on what their troops can do. 

So, I am looking for suggestions on places to eat, things to do in Copenhagen.  In return, I will post about my adventures as I did this spring in Australia and New Zealand and last summer in Germany and France.