Where are you from? And are you studying something that you can get SU from? There are special student housing (called "Kollegium" rooms) in Denmark, where only students are allowed to live. And the rent is considerably lower than normal rental apartments.
It's been a while since I've studied, so my information might be outdated, but feel free to send me an email if I can help in any way. I live in Copenhagen.
I'm from the US. I've signed up for kollegiums and I'm waiting on the list. It's taking a while as all the first year students have priority first, but that's wearing off soon. Hopefully that'll come through soon, but it's going to pose another challenge as I'll be going on exchange in half a year.
It's been a while since I've studied, so my information might be outdated, but feel free to send me an email if I can help in any way. I live in Copenhagen.