[hmmokay]

As I mentioned in another comment, the rent is not particularly high in Copenhagen compared to other cities (although living costs in general are high), and Copenhagen really isn't that crowded. It's hard to have a crowded city in a place where most buildings are four to five stories high.

As for knowing the language: You don't need to learn Danish just to get an apartment - I know a ton of foreigners who got by for years here without knowing a word of Danish. But you do need to realize that one way or the other you have to talk to people - they'll help you find a place or help you translate ads.