My recommendations are:

Søren K: good food, walking distance to Marriott and SAS Radisson hotels, great river view. A good place to celebrate signing of a contract: they have excellent wine list as well as cigars. Located in the Royal Library (also known as Black Diamond).

Peder Oxe: this is the place if you want wild game food. Excellent service. Attractive waitresses.

Blue Elephant: Thai restaurant located in the basement of SAS Radisson Hotel. This is one of the best Thai food restaurants in Europe (they have branches in London, Paris, Brussels, etc.). They even have their own Champagne label.

Any local resident of Copenhagen can tell you the location of these restaurants.