Copenhagen is absolutely charming. I recommend bringing a raincoat and a sweater because it rained every day while we were there. Absolutely stunning city, though. Lots of history and the city is entirely walkable. You can get pretty much anywhere within 40 minutes walking time.
Insider Tip:Bring good walking shoes and don't bother with public transportation. Get to know the city by walking! It's one of the most walkable in the world. You can get anywhere within 40 minutes on foot.