I visited Copenhagen in June, 2019 with my girlfriend. We stayed in an AirBnB that was about a 35 minute train ride from the city center. Housing and food were very expensive there compared to other European big cities. There is a small, but nice & quiet sculpture garden behind the art museum. It's a great place to take a break. The art museum is decent. We went on the free day and it was not crowded. We took a canal boat tour (Netto) which included the harbor. It was nice and they do run you out to the point where the little Mermaid statue is before turning around. It's a way to see it without going out there.
We made a couple of trips to Christiania, the hippy enclave famous for open pot smoking. It's funky, but pot is legal in my state, and I don't partake anyway, so some of the "being bad" aspect of Christiania has worn off I think. There is a pretty large open air bazaar / flea market which my girlfriend liked to shop in. We also went to the Tivoli amusement park and rode the "Daemon", a roller coaster that rolls you upside down. The ride lasted about 1 minute, which was plenty for me.
What I most remember about Copenhagen is being asked to show our train or bus tickets nearly everyday. They really police their public transit there. Also, there's a 7 Eleven on practically every corner. We enjoyed ourselves, but as far as tourist sight-seeing goes, Copenhagen is a 2 - 3 day city. My favorite street food was the spicy meatballs. Sadly, I discovered them on the last day of our trip.