First event this year will be Copenhagen Dining Week.
The concept is simple - go the web page www.diningweek.dk, find a restaurant with a menu you like, order tickets for a time that suits you in week 7 and voila - a night with 3 courses at a nice restaurant in Copenhagen for 200 kroner. Cheap! I went to Gefährlich with my boyfriend last year, beautiful food and very romantic evening. Definitely going again this year. I already signed up for the online ticket queue - you should do the same, as the regular ticket sale have not started yet.
Hope you find something delicious,