8-9 days in Denmark in April

You will be spoiled for choice!!

I suggest taking a look at the Copenhagen Card. It will give you entrance to a number of places and the Discover level has free public transport. You can use that to travel on easy day trips - Roskilde, Frederiksborg Castle, etc.

The many options are indicated on the Copenhagen Card website - good starting point for ideas.
https://copenhagencard.com

I took a first-timer relative in June 2023 for about your same length of time. Our "itinerary" was a simple list of places to see and the days they were open. So much of central Copenhagen is walkable that we were easily able to group attractions in a given area - and move outside that area as we desired. The day trips were taken according to weather and opening days.

Easy planning!

There are many "must-sees" in my opinion - everyone is so different, I won't mention many. However, the National Museum of Denmark is wonderful for history, the various castles in town are all different and worthwhile, Danish Resistance Museum incredibly moving, outside of town, my favorite spot was Helsingør with the Hamlet inspiration castle, Maritime Museum, historic city center, ferry to Sweden. I'm sure I've forgotten some favorites.

adding - I've also spent a week in Copenhagen in April, a few years before Covid. It was a good time with fewer tourists than in the summer.

Sounds like a nice plan. There is a lot of art, architecture and history to see in Copenhagen. But other nearby towns in Denmark worth a day trip are Roskilde, Helsingør, Hillerød. And in Sweden you can also consider a visit to Lund, Helsingborg, Ystad or Simrishamn.

Tourist info provides 11 day trips from Copenhagen with very good ideas.

Tivoli summer season opens April 21 (opening times).

Do not miss to join the Sakura Cherry Blossom Festival for nice photos.

We regularly visit Copenhagen, where our daughter lives. Since there will be fewer tourists in April, I wouldn't worry too much about structuring an itinerary but make your plans dependent on the weather forecast.

These are a few suggestions in addition to the places already named:

• We always enjoy the art exhibits at Cisternerne, an underground art installation space.
• The interior of Københavns Rådhus (City Hall) is very interesting and they do a good tour in English. We have also booked an architectural walk around the outside of the building through Airbnb Experience.
• The Louisiana Museum of Art is another great day trip.
• The canal boat tours might seem cheesy but they are quite fun and a good way to get a feel for the old city.

Also, depending on when you are there in April, many services (like restaurants, grocery stores, and museums) will be closed or have limited hours on Thursday through Monday around Easter. You can easily work around it and plan ahead, but it is surprising how many places are closed compared to the U.S.

thanks to everyone for the ideas!
We will get there after Easter so won't have to deal with those closures. I will take a look at the suggestions and it is good to know that we can be flexible, making plans that are weather dependent.
I had toyed with the idea of flying to Oslo instead, spending 1-2 days there and then taking the daytime train to Copenhagen because I read that the trip is very scenic and different from the Denmark landscape. However I am thinking that there will be so much to see that we should instead just focus on Copenhagen and surrounding area, rather than spreading ourselves to thinly.