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.