Yes! Lovely city, albeit a bit expensive. We went a few years ago, around the time of the launch of the best of Scandi dramas, The Bridge, Borgen, The Killing.
We did all the major sites, walked around the outside of the palaces in the city centre, went inside one of the older palaces but can't remember the name. Other than that, The Tivoli Gardens., The Round Tower, Copenhagen's national museum, Frederik's church. There are some lovely shops and stores in Copenhagen if you just want to browse or even buy. We were staying in Nyhavn right on the canals very central loads of restaurants it was the first time I saw blankets on the chairs for al fresco eating, now they're here too. I really wished we had gone over The Bridge to Sweden, I would have gone a bit further on to Lund beyond Malmo which I believe is quite an old city, I've also heard Malmo is a bit dodgy. We didn't go to Sweden in the end, because we went to a modern art gallery outside Copenhagen called Louisiana which took up a whole day, which my friend wanted to do, but I didn't, and then we didn't really have the time left to do another long trip.
Anyway I hope you enjoy your break from what I understood going over the bridge to Sweden is very doable. The Danish are super nice and they all seem to speak English.