It is best to visit Copenhagen on non-winter or near Summer days. Establishments are mostly close during these days. This is also to make sure that Tivoli is open. Tivoli would have the tallest carousel and some free shows that would surely entertain you.
If you feel sporty, DGI-Byen has indoor pools, spa, bowling alleys and cafes. Nonetheless, you can rent bike and roam around town as your exercise. Bike through Den Lille Havfrue, Christian Andersen’s famous little mermaid fairy tale. Interested in more fairy tales? The Rosenborg Slot is a Disney live castle.
In a matter of true history, the Carlsberg Glyptotek is a great museum that houses different artifacts. Add more history with the Christiansborg is a remarkable palace.
Copenhagen is filled with fairy tales and true stories. More true is the Danish sandwich or the open-faced sandwich should be tried for a reason 😉