We stayed in a great place while in Hamburg, the Generator Hostel (http://www.generatorhostels.com/en/hamburg). It has been a great mix of affordable, clean, functional, fun, aesthetically pleasing, and in a great location next to the Hauptbahnhof (main train station). We really have zero complaints. A few photos....
Having Breakfast - a perfect, simple example of German Breakfast
The group outside on our way to Uni Hamburg
Dr. Stacey Fitzsimmons leading a discussion in the lobby