You cannot blame me for constantly trying to entice you to come to Nørrebro. This is the coolest neighborhood in the world (both according to me and according to Timeout). And the best drinks are served at The Barking Dog.
As with all cool places, you must know it exists in order to find it. It is well hidden in a basement on a side street of the busy Ravnsborggade. The drinks are ordered and served at the tables, always with the sweetest coasters. This is a proper high-end cocktail bar, but with the local, rough atmosphere that only Nørrebro can give you. The drinking menu changes regularly, but my favorite Paloma always manages to stay on the menu. However, I would recommend you stay out of the Chipotle Negroni, that drink is seriously hot!
Bring some friends or just catch a seat in the bar and make friends with the bartenders. No need for high heels or any of that stuff, just be you and enjoy your drinks. When the bill gets too expensive, leave for the nearby bar Kind of blue, and continue your night there.