We were looking for a hotel on Østerbro in Copenhagen as it was located near our conference. We found Hotel Østerport online and booked directly on their website as they offer free breakfast included in the price if you book directly on their own website.
To our delight, we found out that we could take the train directly from the airport to the hotel. The train stops just across the street from the hotel, only a 100m walk. Breakfast and service of the staff were super. All in all, we had a great stay and would recommend it if your looking for a hotel in Copenhagen. If I should mention any issue with the hotel, then it would be that the train noise can be an issue for if your a light sleeper.