First thing: Copenhagen is the most expensive city we've stayed in. I managed to get decent rooms for around 50-70€ in London, Paris and Barcelona, amongst others, but Copenhagen was by far the dearest.
I've searched a lot before booking and it turned out that if you want to sleep in the city and wanted a room with bathroom you had to shell out at least 120€ for 2 people a night.
So I took the Zleep. Here are the facts and you decide if it's for you:
+"relatively" cheap
+100m from train station. 3 min to airport, 8 min. to city, frequent trains
+clean enough
-the beds: every movement of either of us woke me and my girlfriend. And they're terribly soft. Normaly I can sleep everywhere, but these are just the worst beds I've ever slept in.
-noise: one night I could hear the TV from another room, the next I could hear my neighbour snoring. Again, I'm not at all sensitive to these things but these walls are just paper.
-the shower is practically over the toilet, you have to be very nimble not to put everything under water.
I personally have stayed at dirt-cheap hotels like Etap in Germany or Travelodge in the UK and would go there again to save money. But because of the terrible beds I wouldn't go to the Zleep again.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC