My daughter is currently living in Copenhagen while working on her Masters at DTU. We visited a week in March. We rented an apartment through Airbnb and had our daughter stay with us. She was on spring break. Restaurants are very expensive, so we ate in most of the time. We had lunch at a restaurant near Nyhavn for lunch , Told & Snaps, which was fantastic. We also had lunch at one of the restaurants in Tripoli, Restaurant Groften, which was great also.
Definitely do the Free Walking Tour of Copenhagen. It meets in front of the Town Hall (near Tripoli), and you pay what you think it’s worth at the conclusion of the tour. Try to do this tour your first day to get the overview of the city. Because it rained almost every day we were there, we didn’t get to do it until our last day.
Visit Nyhavn, Paleis Christiansborg (tower which gives magnificent view of the city), Natonal Museum of Denmark, and the Rosenberg Castle. There are two other places I can’t remember, but I’ll text my daughter and get back to you.
Be prepared for damp, windy, rainy weather. I packed based on the projected temperatures, and I froze. In March, I should have taken a long very warm winter coat, hat gloves, and rain boots. Also wear lots of layers.
Please feel free to PM me for more details.