Don't know if it's unique,But here's a bit of what Copenhagen has to offer.
We have city bikes you can rent, They're partially running on electricity, Saves you a bit of enegy when going uphill
And then there's the Red square (It's actually painted pink)
with swing sets where you can lie down while you swing, Comfotable and a bit weird
In the summer time its also used as an outside cinema showing B or low budget movies, Until 5am in the morning.
And then there's Christania if you're longing for some weed, All the stalls gets removed once a year by the police, Come back next month and they're all back again, Its been like that for over 30 years now
And we have our very own Red light district called Istedgade as Marcel mentioned
, Riight next to copenhagen central station (Very convenient)