As you know: I love libraries and sometimes I go to the one at the UKE, our University hospital. Of course they need to provide for students and professors and some years ago they opened a rooftop pizzeria. I like the place as the student spirit melts with cheese and pizza, as I do the rooftop terrace, which, of course, can be a little windy in Hamburg. Try to go with someone to get a big pizza and share it. It is big enough for two eaters.
The buildings on the big hospital campus have a letter and number code and the building is N19 and it is on the 4th level, just around the corner from the library. If you are already on campus, check the nearby medical museum (check out my article), too, once you are there. Or the Eppendorf neighbourhood which is green, relaxed, and sometimes a little posh.