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This classical mansion on Kongens Nytorv, is home of several cultural institutions, like the Royal Danish school of Visual arts, and has an art exhibition space, with changing, often world class, expositions - check the schedule at their website.
Charlottenborg Palace is a large town mansion located on the corner of Kongens Nytorv and Nyhavn in Copenhagen, Denmark. Originally built as a residence for Ulrik Frederik Gyldenløve, it has served as the base of the Royal Danish Academy of Fine Arts since its foundation in 1754. Today it also houses Kunsthal Charlottenborg, an institution for contemporary art, and Danmarks Kunstbibliotek, the Royal Art Library.
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The Royal Theatre
A majestic old building on Kongens Nytorv, houses ballet, for which the theatre is world-renowned, and drama performances. There is a 65% discount for those under 30 on selected performances, to encourage young people to see the classic arts.
On a sunny day, this is a top spot for oozing in the sun on the bulwark with a beer from the supermarket, or at the outdoor serving areas of the many (rather expensive) restaurants and cafe's dotted along the "sunny side" of the canal. For any self-respecting Copenhagener, this is a top priority on the first day of spring; while at the height of the tourist season, it is mainly left for the visitors to populate. Often there will be street performances, mostly improvised music concerts, somewhere along the canal - take a seat, and relax.
New Harbour
Nyhavn is a canal leading from the main harbourfront all the way to the Kongens Nytorv square, lined with colourful historic buildings. It was built to originally be what the name says - Copenhagen's new harbour. Over time, it became too small and lost its commercial and transportation importance, and in the 1970s it was designated as the historic port area, where historic boats and their replicas are moored. It is immensely popular with tourists and locals due to its picturesque nature and is full of restaurants, cafes and bars offering waterside gardens. Consider visiting in the evening to avoid the crowds, as it can become extreme during a sunny day. The restaurants lining its sides are rather expensive and have few vegetarian options.
Nikolaj Kunsthal
An old church housing changing contemporary exhibitions from newer Danish and international artists. Visiting will take about an hour and is well worth it if you like contemporary art.
A museum about the psychology, history, and geography of happiness—and why Denmark is often ranked the happiest country in the world. Created by the Happiness Research Institute, an organisation that studies happiness with the goal of improving people's well-being around the world.
The Royal Danish Playhouse
A 1000-seat national stage for the dramatic arts, with 3 stages. Opened in 2008, its beautiful piece of modern architecture overlooking the harbour. Even if you are not going for a play, the cafe in the foyer, Ofelia, is a nice place to sit and enjoy the view over the water and Christianshavn.