Thanks everyone for all of the suggestions. Based on your comments, I'm sure that the Scandinavia isn't the right choice for me-- I'll take a look at all of the other properties that people mentioned to see which one sounds best.
Per the last comment from maize&blue- I did think about the Hilton, as I'd get benefits and points there, but thought that staying outside of the city and having to take the train back and forth might detract a bit from the experience of being in Copenhagen. It does sound like the train runs very often from the airport, but I figured between waiting time and train time, I'd be looking at ~20 minutes each way, each time I had to come or go from my hotel...
Someone please chime in if my assumption is incorrect on this.