Dogs in Copenhagen

Hi!

My name is Stephanie and I live in Brooklyn, New York. I may have an opportunity to live in Copenhagen for about 5 months this spring. I have a German Shepherd who is too much a part of me to leave behind. Does anyone have any advice about how to find an apartment that takes a dog that size? I am interested in living in the city center. Also, how dog friendly is Copenhagen? In my neighborhood I walk everywhere and he is usually with me. If I need to go into a store that doesn't allow pets I just tie him up out side for a few minutes. It's never a problem.

Thank you!