We loved Copenhagen. Spent 5 days there in August after 5 days in Billund at Legoland. Got train from a Billund to Copenhagen. We found plenty to do and go train / bus to Roskilde Viking village/museum and ships - you can go on a replica ship. We loved Tivoli as well. Hugely expensive but we really enjoyed our time there.
We spent 3 days there which was just right. Really liked it. We did: Tivoli with friends so a whole day nearly Nyhavn mooching and then a Netto boat trip Rosenborg castle Papiroen Street food - great food and people watching Got the train to Humelbeck to the Louisiana art gallery. You could also get the train over The Bridge to Malmo
We went last Easter, DC were 5 and 8. We went Tue-Fri - 3 nights.
We did, roughly - 1/2 day Tuesday - Potter around city, lunch, Potter, dinner, buy Copenhagen cards. Full day Wed - National Museum, Tivoli Gardens, we spent hours in Tivoli. Apart from thrbfinfsir, here is a good playground (the pancake house in the whale is not great thigh). Full day Thursday - Boat trip (to Little Mermaid), Up the towww at Christiansborg palace, design museum, botanical gardens, geological museum (DH and I are both geologists!!) Most of day Friday - back to national museum, Changing of Guard at the Ameliabourg palace, Lego shop
We could have easily spent more time there, but it is very expensive!
I’d recommend getting a Copenhagen card each -free entry to loads of places. free bus and train travel, boat trips.
We stayed at the Hotel Ansgar, which was well priced and central. Big family room (double plus 3 singles) ,excellent buffet breakfast.
If you have slightly fussy eaters, and a non-meat eater with you, we found a super “artisan” burger restaurant, Friends &Burgers which kept everyone happy. We had a couple of picnic meals too.
I agree. We barely used the card for public transport (train to and from airport, one or 2 buses in town), but we used it for free entry to pretty much everywhere we went and a boat trip. In fact 2 - we squeezed another one in in our last day. I did some rough sums, the cards saved us around £100.