I spent a night or two in Copenhagen when I drove around Europe in 1996. It's a very pleasant city, and very easy to get around.
When I was there, a flotilla of tall ships was tied up at the harbour, and you could go aboard and have a look around - never having been on a tall ship it was an opportunity not to be missed, and I got on board a Russian boat called Mir. But they didn't allow me to climb up on the rigging!
Just around the corner was the statue of the Little Mermaid, I must admit it wasn't what I was expecting. I thought that it would be a bit bigger, or a bit further out from the shore line. At least I got another in my series of "famous places looking bad" - the Mermaid with the oil refinery in the back ground.