My wife and I flew to CPH for a long week end this past spring. Had a marvellous time. We stayed at the Copenhagen Admiral Hotel. It is a converted grain mill down at the harbour. Our original booking was a semi-suite but we did not stay in it as it was two floors and seemed small, with the bedroom on the second floor with no windows. So we moved to the senior suite, of which there are two. just wonderful, great view of the ships sailing to Sweden and Norway, mind you it cost too much but wee get so little time away, it was well worth it.
Another excellent choice, 5* is The Angleterre. It is situated in the town square and is your typical older grand hotel. Even if you don't stay here, you should go to the bar. there are photographs of their guests from Raymond Burr to Dwight D. Eisenhower. And I am telling you we met a fascinating character there1
Go down to the port where the naval ships tie up, they will let you on their submarine if it is in port.
Have fun.