Must see things in Copenhagen in three days - well there are a lot of things going on. But of course n depends on your interests.
I always recommend fotografiskcenter.dk - a small photography exhibition place in central CPH.
This guide is in English http://www.aok.dk/english
It’s quite easy to get around in CPH - it’s not that big. You can see walk around the city center including Nyhavn (lot’s of bars and restaurants) in a few hours.
Visit the neighbourhoods outside the city center Vesterbro, Noerrebro and Nordvest.
The public transportation is quite good and brings you any where pretty fast.
Go north by train and visit Louisiana art Museum - it’s very popular so there’s a lot of people - but worth the visit.
Then there are Tivoli Gardens in the center (pretty expensive entre fee) and north of the city Bakken (very old amusement park - no entry free. It’s located inside a huge forrest like public park.
Enjoy your stay…