Dyrehaven, Denmark - Polarsteps
After breakfast, I highly recommend you head straight out of the city on the train up North to hit 3 landmarks in the same day. Start off with the deer park. This is a 1000 acre park where thousands of deer roam free. It's very picturesque. There's also a beach with views of Sweden which we walked over to, and the self-proclaimed world's oldest theme park, Bakken, is also in this park, though we didn't make it over there.
It's a lot of walking so on arrival, you can get a horse drawn carriage for what I'm sure is likely a prosperous amount of money. If you walk through the park, when you come out to the other side, you can chat a bus straight up the coast to the next 2 attractions but you must time it well since that bus only runs every hour! (We didn't time it well...)
Long Weekend in Copenhagen