Of course everyone knows about the Reeperbahn. That includes British stags which have more recently been hitting the city. So you may be wishing for something a bit out of their way:
– Hamburger berg, a street just off Reeperbahn with plenty of chilled bars and some with a bit of music to dance too.
– Schanze area, chilled out bars, and on a recent visit it seems new beers are hitting the taps, some bars feature a “beer takeover” which is a nice change to the typical stuff. The best area is around the Schukterblatt. try Saal II, Bedford Bar and Kulturhaus Ill&70.