Hope you don't suffer too much because of the Danish summer weather! In case it decides to behave well, you can go to Tivoli tomorrow (thursday) to celebrate it's 170th birthday! When Tivoli first opened in 1843, all it had was a rollercoaster an a carousel - luckily, there's a bit more going on there today!
There will be lots of stuff going on, mostly with the Tivoli Guards! Most importantly, there will be fireworks at 22:45 - which you can watch for free outside the gardens, so if you happen to be around the centre of Copenhagen, look to the skies at that time.
Unfortunately, Tivoli is still as expensive as always to go to - no birthday offers. :)