Book ahead for lunch at Tårnet, owned by prolific restaurateur Rasmus Bo Bojesen and memorably set inside Christiansborg Slot's commanding tower. Lunch here is better value than dinner, with superlative, contemporary smørrebrød that is among the city's best. While the general guideline is two smørrebrød per person, some of the à la carte versions are quite substantial (especially the tartare), so check before ordering.
Enjoy your post-prandial coffee sitting on the dining room steps, which look out over the castle courtyard and Tivoli Gardens. Interesting tidbit: the pair of lions looking down on the dining room were originally covered in gold and used as props at royal occasions. The gold melted during the palace fire of 1884.