Glyptotek museum if you like museums - it's a good one and the name is one of my favourite words in the world! 😂
The Kongelige Bibliotek, (black diamond building) is a spectacular building.
I also like the Rundetaarn (round tower) if you don't mind walking up hill to get to the top of the tower - great views and there are often special exhibitions on too.
Simply strolling down Strøget is nice if the weather is nice - it takes you right to the harbour (Nyhavn) with lots of lovely bars and restaurants.
Amalienborg and Rosenborg palaces, the design museum and the little mermaid statue are all nearby and it's a nice walk if the weather is good. Be warned though that the mermaid is tiny and the wind can be really biting walking there - hat and scarf essential.
Carlsberg is a bit further out - you can take the tram or walk. Nice brewery tour and museum.
Copenhagen is a small city and if you wanted to, you could probably see all these in the 2 days if you put your mind to it but its also a wonderful city for just bimbling around and stopping for coffees, walking round parks and taking a look at whatever strikes your fancy.
I used to live there and I'm super jealous of you as I live on the other side of the world now and don't get back very often. Have a wonderful time!