The new Opera House, built in 2003 just across the water from the city center. A modern venue for operas, ballets, concerts-- y'know, lotsa arté 'n' stuff like dat for ya.
The even newer Skuespilhus or "Playhouse" for theater productions
Det Kongelige Teater, the old Royal Danish Theater on Kongens Nytorv; once the only place to go for theater and opera, now looking for a new role to play.
Ludvig Holberg (1684-1754), the "Shakespeare" of Denmark, wrote most of the classic Danish comedies & plays performed in det Kongelige Teater.
Palads Movie Theater. One of many in Kbh. Movies are popular here of course, and there is always a selection of Danish and other European films to compete with the American blockbusters.
Note : foreign films (like American) are not dubbed in Denmark, but undertexted, original language always intact. Most larger European countries dub in their own languages--French, German, Spanish, etc--which ruins the artistic integrity of any film. Scandinavia and Holland don't do it, so a traveller can enjoy many films in these countries. Being countries with small language pools, they tend to become familiar with other languages anyway.
Fantask Sankt Peders Stræde 18, 1453 Kbh K
This is my favorite comic book store, where I can keep in touch with the super-hero universe and its commercial market, being a comix artist myself. Fantask has most of the mainstream American and British stuff in print: Marvel, DC, Dark Horse, ABC, Image; in English or Danish. They also have most of the popular large-format French/Belgian comic albums in Danish translation: Hergè, Cothias, Burgeon. And of course, Japanese Mangas. We're talking about REAL Culture here.
Free theater in the park called Kongens Have. This one's for kids.
Ever heard John Wayne say: "Ein mann macht was ein mann machen mussen"? Or Toshiro Mifune say "Merde" instead of "-shaw!"? The only time I ever saw "My Fair Lady" was when I was a GI in Germany...I still remember how "woverly" was translated as wunderschön.