I have never been strongly interested in Berlin (either zoo) because exhibit quality is important to me and I hear it is lacking (especially for my beloved cats). Still I could feasibly combine it with Vienna...
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If you want to see the main sights, Berlin can be seen in a day. I spent two full days there. I had a walking tour with my hostel (Amstel house, would recommend extremely highly) which took me from Moabit, to the Hauptbahnhof, the Reichstag, the Brandenburg Tor, the Holocaust memorial, the Sony Centre, the Wall, Checkpoint Charlie, the Opera house/church, the museums quarter and alexanderplatz. I also managed to see the topography of terror. If you would like to spend an extended period of time in museums (DDR, CPC, Museum Island) you may need more than a day. On my second day I went to the Zoo which, in my opinion, if you are brisk and not fussed with photograph (both of which, understandably, I doubt you are) then you will be able to do it in 6-7 hours, but that does not include the birdhouse or the aquarium.
If money was no object, I would recommend doing Vienna, getting a train to Prague and seeing a few of the Czech collections, going on to Leipzig and then Berlin. An EURail pass would come in handy here. Prague is a lovely city which I would recommend allocating at least a day to exploring, while Vienna, while good, I would not suggest is a loss if you did not have time to explore the city.
If non zoo related attractions were also high on your list for the trip, I think the above, as well as the tour of the Low Countries already stated would be extremely good. Amsterdam is my all time favourite city.
Hope this is helpful, if a bit dreamy.