Copenhagen's main train station. As a general rule, the bigger the city, the bigger the train station.
One of the entrances to Tivoli is across the street from the train station. I don't know which was built first; I suspect Tivoli opened a second entrance for the convenience of visitors arriving by train.
Copenhagen is a bicycle-friendly city. Everywhere you go there are racks of bicycles that are essentially free for the taking... almost. Insert a 20 DKK coin (about 3 USD) and the bicycle springs free of its lock. When you're done, when you've arrived where you need to go, find a similar lock and reconnect the bike; a 20 DKK coin is returned to you. Can't find a lock? That's not a problem; simply abandon the bike right there. A homeless person will take the bike and find a place where he can receive 20 DKK for his efforts.