Budget
Copenhagen Airport Hostel
A homey, if a little run down hostel. It is run by two young guys, with downtown just 15 minutes away by the metro which is 30 Kr each way, unless you buy a discount card. Also note that they charge an excessively for renting out linen.
Midrange
Hotel Amager
Modest two star hotel, fairly centrally located near the bridge to Christianshavn. Rooms can seem a bit antiquated, but the staff is nice and there is free internet.
Dragør Fort
Unique accommodation in an old fort from 1915. Renovations to turn this into a event and conference centre are ongoing, and the owners have created seven fairly nice and big double rooms in the process — each with television sets and private bathrooms.
Dragør Badehotel, Dragør
Charming old beach hotel from the last century, recently renovated, in some beautiful traditional buildings.
House of Colors
Not quite your ordinary apartment rentals; in a 19th-century house situated in a quiet neighbourhood. Features 3, nice, colorful as the name might give away one bedroom apartments with full kitchen, dining table and a small living room. Also has a lovely little garden with tables and free use of old but serviceable bicycles.
Hotel Copenhagen
Although this can seem more like a hostel at times, with shared showers and toilets and rather crammed rooms, it is a good price for Copenhagen and there is no curfew, but a doorcode for the door after 11PM. Good staff. There is one computer for internet access.
Zleep Hotel Airport
Basic two-star no-frills hotel, that gets the job done if you want to sleep near the airport for a single night at a reasonable price. Prices can get as low as 299 Kr if you book more than 60 days in advance.
Copenhagen Camping
Brand new camping grounds on the southern tip of Amager opened in 2008, within walking distance of a beach.
Finding accommodations on Amager can be a good alternative to the morebusy parts of town, near the central station. There are a few budgetoptions available here, and it is fairly quick and convenient to get to the sights in the city centre, while also being more peaceful and laid back. The options located on the southern part of the island are interesting, with beaches, forests, fields and some historic locations right outside your doorstep — but it also takes you a good 30-40 minutes to get downtown, unless you have your own wheels.
Hilton Copenhagen
Five star hotel located adjacent to the airport, with all the facilities you'd expect from a Hilton hotel, and very convenient for those arriving after many hours traveling.