Kongens Nytorv offers more fine dining . There are restaurants like 'Fiat', 'Ravage' and 'Bistro Royal' which are of high quality but rather expensive.
Around Kongens Nytorv you can more or less do everything. Visit Nyhavn, stroll down Strøget (a long shopping street), find bars and exclusive restaurants, do some sightseeing and everything in between. This is an excellent place to start your Copenhagen journey.