Operaen is something of an institution. If you duck past the dealers in the stairwell, take the stairs to the first floor and go through the door, you'll be treated to one of the coziest experiences on your visit to CA. During the day, it's a cafe with a limited food selection; at night, it becomes a venue, presenting all kinds of genres.
It's without a doubt one of the nicest places in Copenhagen. Prices are very reasonable and the food, when they have it, is great. At you can see concerts most days of the week, and the weekend-parties go 'till early morning.
No website, but they post their monthly program all over the city. And you'll find it when you're there.