Day and a half in Copenhagen

Don't waste time going to see the Little Mermaid statue if it is mentioned in the book.

One lovely way to get a overview of the city is to take a canal cruise. You’ll get sight of many of the architecturally interesting buildings and other landmarks. We bought tickets at the TI office.

I really enjoyed Rosenborg Castle - it's a beautiful little place and the Danish crown jewels are in the lower level.
Stolling along Nyhavn Harbor is nice...you can take a boat from there to cruise along the canals. Lovely!
You can walk through Amalienborg square where they royal family lives in several palaces.
A nice place to stop for a break and a snack / coffee / tea is the garden of the Design Museum Denmark...it's just around the corner from Amalienborg and you can sit in their beautiful garden - it's very green and pretty and is a nice place to rest and relax. They have a cool shop with lots of Danish-designed objects and, if such things interest you, they have a whole museum full of it.

I support Rosalyn's suggestion of a canal cruise, but if you are a little adventurous you could try https://en.goboat.dk/.

If you will spare an afternoon you could visit the oldest amusement park in the world: https://www.bakken.dk/english/. Founded in 1583. The English version is not very good but you take an S train to Klampenborg and follow the crowd. Use https://www.rejseplanen.dk/webapp/index.html?language=en_EN to plan the trip.

Another vote for the canal cruise. Visit pretty Nyhaven.
Have a smorgasbord lunch. Skip Tivoli.

My husband and I also enjoyed our canal cruise and I second Rosenborg Castle. We also enjoyed wandering Tivoli.