We strongly recommend you Ben's appartment: Ben made the necessary so that we could easily pick up the keys when we arrived as he wasn't in Copenhagen during our citytrip.
His appartment was well-decorated, super clean... we immediately felt ourselves at home! Moreover, thanks to its central location, we could easily discover the whole city by foot starting from his appartment.
Finally, the city guide Ben left for us allowed us to discover among other things a tiny Italian restaurant in which food was just amazingly good!
Thanks for eveything Ben!! :-)