I have stayed at two hotels in Copenhagen and enjoyed both.
The first is Hotel Bethel on Nyhavn. This was on a RS tour. It looks like the hotel has been combined with the building next door since I stayed there. Please note that some of my tour mates did not like this hotel. They felt the rooms were not well appointed and that there was too much noise from the street outside. There were a lot of high school graduation celebrations going on. My singe room was clean and comfortable and I enjoyed the views of the water from my room. I slept with my windows open and I was not disturbed by noise.
The second is Hotel Axel Guldsmeden. This hotel is close to the train station. It supposedly is in the red light district. I was traveling alone and was very comfortable walking in the area. The rooms are beautiful. There was no street noise in my room and I slept with the window open.
Enjoy your trip!