My host sister, Stine, and I visited the 104 year old theme park situated in the middle of downtown København: Tivoli. We were SO lucky, we had a beautiful sunny day, an afternoon where neither of us had class, and free passes to get in! (Stine had a season pass, I had a DIS discount) The rides did cost us 205 kr. but they were definitely worth it! We barely waited in line, and we got to try all the rides.
These are two of my favorite: on the left, "Vertigo" and flying swings on the right. They are 30m and 50m high. You can get some really nice views of the city up there! If you're not terrified the whole time anyway. I definitely was on Vertigo! That ride has an "interactive" option (which we opted out of!) to control the plane on your own, so that it twists and turns and goes backwards.
But besides the rides, the park is actually very pretty. There are lots of fountains, lakes, gardens, birds (including a peacock!) and even a ship you can eat dinner on. There a lot of very nice restaurants, Hard Rock Cafe Copenhagen is there, and cute shops everywhere. We didn't spend any money besides our ride passes...og en is!