We highly recommend Hotel Skt. Petri. In the central Copenhagen neighborhood of Latinerkvarteret, this hip hotel is 300 meters from shopping street Strøget, a 6-minute walk from Torvehallerne, the Nørreport metro station and the 17th-century castle of Rosenborg Slot. And a 14-minute walk from the Statens Museum for Kunst national gallery.
Bonus tip: They have the best pizza restaurant on the ground floor.