Copenhagen Off The Beaten Path Tips by Secondhandviking

A green breather?

Denmark has absolutely no hills to boast (Highest point is 164 meters above sea, I think)so you should go for the beach instead (of which we have a lot!!) It is quite easy to get to a great beach from Central Copenhagen. Easiest is if you go south. Take S-train line A direction Hundige and get off at Brøndby Strand (15 minutes from f.ex Central station) . From the station it's a 5 -10 minutes walk to the beach (just go with your back to the communist looking highrise in kinky colors :-D you cant miss it..
Or you can continue by train to Ishøj. The walk from the station is longer (there might be a bus connecting.. www.rejseplanen.dk can tell you) Then you can combine contemporary art and a day at the beach. This plan has an advantage: You never know about the summerweather in Denmark! It can be cold and windy or the sun is shining from a blue sky..Or both within hours. Be prepared for windy on all accounts..
If you are feeling energetic, then rent a bike. You can bring it on the train for free.. There's a beatiful bicycling path from Ishøj, past Brønshøj Strand almost to city centre - most places right next to the beach. By June there should still be some roses blooming. And a couple of places to buy ice-cream on the way..

In central Copenhagen, Kongens Have (Next to Rosenborg Castle) is within fairly easy reach from most of the sightseeing. A great place to have an ímprovised picnic and do some people-watching. You can bring a blanket and have a rest there. Many other people do.
Assistens Kirkegård is a cemetary/park. It is very old and many Danish "celebrities" are buried there - for example Hans Christian Anderson. People use it as a park and a place to picnic. Might sound morbid, but it is really charming with a lot of old trees. On a windy day it is great. If you happen to be sightseeing in the neighborhood, go there for a breather. It is also ok to lie down and catch a nap on the grass as in most other parks.

On a sunny day Frilandsmuseet in Brede might be just the thing for you! Personally I love this place. It has a collection of old houses from the various parts of Denmarks countryside, complete with little cornfields and gardens and brooks - 200% idyllic and you can see as much as you like or just camp somewhere in the grass and enjoy the silence.. ADMISSION IS FREE!

Website: http://www.natmus.dk

Dissapointed by the little mermaid?

That's understandable! I think most Danes would agree, that she is just too small and too nondescript to deserve the attention she gets.. Not that I begrudge her any, but there are so many other great sculptures to see!
There's one here, that is so powerfull and expressive, that it litterally gives goosebumps everytime I see it..
You can find it in Glyptotekets garden (right next to Tivoli) and admission to the garden is free. It is called "Troll smells cristian blood" and it is spooky! The pictures doesn't do it justice, you have to go see it for yourself.
It was done by Niels Hansen-Jacobsen 1896 and bought by Carl Jacobsen (founder of Carlsberg) He bought it for Jesuskirken in Valby, where it was supposed to counterpart a large crucifix. It symbolizes the evil in the world, and my guess is that the citizens of Valby found it a tad too expressive, as they just didn't want it near their church. It was then put in the garden of Glyptoteket..
100 years later a copy has been made and put at Jesuskirken in Valby as originally intended, so you can also go see it there, if you feel like it..

Website: http://www.glyptoteket.dk

Best place to go with a hangover: Glyptoteket Museums & Exibitions Review

The "Ny Carlsberg Glyptotek" was founded by Carl Jacobsen, who also founded.. Carlsberg! Which is why you should go see this collection of sculptures after a night in the company of Carlsbergs.. The museum is just the right size. Not too big, not too crowded and the main hall is soothing. You can sit by a sculpture called "Vandmoderen" (the wather mother) and just wait for your hangover to dissipate.. And ADMISSION IS FREE ON SUNDAYS!
Originally Glyptoteket was Jacobsens private collection of Danish and French art and also antiquities from the Mediterranean. It has different (quite interesting collections) and is easy to find just next to Tivoli.

Website: http://www.glyptoteket.dk