Had an awesome stay at Karen's, right in the heart of vesterbro.
Perfect location, really homely, loads of space for two people, clean, interior was really cool as well. All in all we loved the place ... also has a comfortable outside terracy area which we used quite a bit.
Karen made us feel very welcome, even left us a few beers and bits and pieces to get us going. Her recommendations were spot on and aided our explorations.
Highly recommend this for anyone looking to stay in Vesterbro.