Excellent choice of city, Copenhagen is without doubt my favorite Nordic capital. I live only an hour away so I try to go there as often as possible.
The Danes have a thing for french food and wine-50% of all wine sold in Denmark is french- so be prepared for that.
, great food and excellent winelist.
, french/Danish food. They only serve a set 5 course menu. Ate there a year ago and was very pleased.
Slotskalderen hos Gitte Kik, you can't visit Denmark without having a smorrebrod(open sandwich). Imo you get the best ones here. Open for lunch, make reservations +45 33 11 15 37
Aside from food and wine, i recomend a visit to Christiana
. A community within the city founded by hippies in the early 70s. Most famous for "Pusher Street" where you could buy marijuana in the open, authorities were simply looking the other way. This trade closed a few years ago. The architecture alone is worth a visit, so make sure to go now before Christiania is just another generic neighborhood.
That's what I could think of for now.
Oh, almost forgot, make sure to have a glass of Gammeldansk, a (very) bitter spirit and extremly popular in Denmark. They drink all hours of the day, sometimes with breakfast.