(Copenhagen) — I’ve only been to Copenhagen a couple of times, so only have limited experience with hotels. But here’s what I found, some I’d recommend, others not.
Have you seen the Hotel Nimb? I’ve never stayed there, but I walked through it. Cafe Nimb is very fancy. There’s a more casual brasserie that I loved eating at. Very open and lively. Expensive.
http://www.tivoli.dk/nimb/

We stayed at 71 Nyhaven which was a decent place, more of a business hotel. But nice rooms, comfortable, good location, decent value.

The 71 Nyhavn hotel is a nice comfortable place, in a good location at the end of Nyhavn, right next to the harbor.

Across the Nyhavn

http://www.tripadvisor.com/Hotel_Review-g189541-d207305-Reviews-71_Nyhavn_Hotel-Copenhagen_Zealand.html
I also stayed at the Skt Petri (don’t ask me how I pronounce it).  I thought it was way over-priced for what you got. I wouldn’t recommend it so much.
http://www.hotelsktpetri.com/

Stayed one night at the FRONT, which is a Scandic hotel, which are usually very spartan.  This is a spartan hotel trying to act like a boutique hotel. Decent enough, but meh.
http://www.scandichotels.com/Hotels/Countries/Denmark/Copenhagen/Hotels/Front/?hotelpage=overview

I think I once looked at the Admiral Hotel and it looked decent.
http://www.tripadvisor.com/Hotel_Review-g189541-d229647-Reviews-Admiral_Hotel_Copenhagen-Copenhagen_Zealand.html

Here’s Monocle’s guide:
http://www.monocle.com/upload/Volumes/01/2525/Rolex/Business/Copenhagen.pdf

The Bertram’s looks really cool. I’ve read about it a bunch:
http://www.tablethotels.com/Bertrams-Hotel-Guldsmeden/Copenhagen-Hotels-Denmark/113121?depDate=&nA=1&arrDate=&nC=0