We enjoyed our time in Copenhagen, but Denmark is an expensive country. For our visit, one USD bought 5 Kroner. That meant three sandwiches at Subway cost $40.
Penny-pinching aside, the reason to visit this city is Tivoli. While it is one of the oldest amusement parks, it's quite possibly my favorite. It has character, and not the animated variety. Also unlike Disney, there's no need for a weeklong stay to see and do all it has to offer. Certainly, you could spend more time at Tivoli, but you'll manage to see and do most everything at the park in one full day. It is busy but not overcrowded, and this means short lines for all rides and attractions. Plus, Tivoli is particularly lovely when illuminated at night.
As for the other major attractions: Nyhavn is where locals and tourists drink and socialize, The Little Mermaid is an out-of-the-way tourist trap, and Stroget is just one more shopping street. But they're nice to see anyway.
We also visited Rosenborg Slot, its treasury, and museum. They provided an interesting account of Danish history. For more, be sure to see the Nationalmuseet and Kastellet, and even the Copenhagen Amber Museum.
Speaking of amber, do check out the House of Amber. They sell beautifully handcrafted pieces of jewelry and make very special souvenirs.
And did you know LEGO is pronounced lee-go, not leg-go?