What Are The Best Tourist Attractions In Copenhagen?

Copenhagen has a variety of attractions.  There is the world famous Tivoli Gardens, which is a large amusement/theme park, with some spectacular gardens.
There is also the Christiana neighbourhood which is the residual remains of a social experiment of a 'hippie village' set up in the 1970's.
There is of course the Little Mermaid statue, which is nice... but some think over-rated.
In addition, there is a good range of shops, as well as some castles such as the Rosenburg Castle and the Amalienborg Castle.
As one might expect, there is also a little culture and some really quite spectacular Museums, such as the Glypotek Museum, which enjoys a worldwide reputation.
Denmark is also famous for producing porcelain, furs (!) and crystal and all of these can be viewed/purchased in Copenhagen.
The food is also sufficiently different from the UK and US, to make eating out a tourism experience in itself.  Prices can be a little high and it can be cold in winter, but is well worth a trip !