The metro runs directly from terminal 3 to Kongens Nytorv. Get off at Kongens Nytorv and walk to Copenhagen Strand Hotel in around 8 minutes.
Taxis from the airport cost around DKK 250. All taxis run on a meter and accept dankort and most major international credit cards.
There is a free bus line 20E from terminal Dampfærgevej via Østerport Station to Kongens Nytorv outside Magasin du Nord, where you can go to the hotel in five minutes.