As opposed to Romelle I would always opt for the non-US airline. US airlines are te worst in the world in my, and most others opinion especially when compared to their Asian counterparts.
If you're not collecting points anywhere specific I would opt for SAS. One of my favorite Copenhagen hotels is the Hotel Front. Central location, great rooms which are modern and stylish. St Petri is anoter decent option; they are part of Design Hotels. If you want to be by the airport the Hilton is pretty nice.
www.hotelfront.dk