The Playhouse, which is part of the Royal Danish Theatre, is a recent construction in Copenhagen, which, as the name indicates, is where you go when you want to see a play.
Personally I must admit that I have never seen a play here, but I often come here when I'm in Copenhagen during summertime, since the house has a great outdoor area with a cafe and restaurant. Outside on the deck you can go for a walk, or you can sit by the tables and enjoy the sun and the view over the canals, and just across the water you find another architectonic jewel, the Opera House.
Remember to step inside and see the house. The architecture is amazing, and the building is really worth a visit - with or without plays.
Sankt Annæ Plads 36. www.kglteater.dk