There are various hotels nearby the arena, with the closest being:
Hotel Hilton airport ( distance from venue 1.7 km)
http://www.hiltonhotels.com/da_DK/danmark/hilton-copenhagen-airport
Hotel Park Inn Radisson airport hotel (distance from venue 2.4 km)
http://www.parkinn.com/hotel-copenhagen
To find alternative accommodation you can visit www.visitopenhagen.dk which is the official tourist site of Copenhagen and has many options for staying in and around Copenhagen and Tårnby.