Every year in August, the Copenhagen Cooking festival offers a range of interesting and delicious events. Someone came up with the glorious idea that the festival shouldn't be reserved for summer, and cooked up a winter version.
There is a multitude of events to choose from, but my favourite is the Copenhagen Dining Week. For one week, 50+ excellent restaurants offer 3 courses for DKK 200 per person! You can read more about the restaurants and their menus here, and buy your ticket for a great meal at a very reasonable price.
I personally recommend L'altro, LêLê, Magstræde 16, NIMB Brasserie and Orangeriet. But looking at the list of restaurants, I don't think you could go wrong anywhere. Enjoy!