Germany is my favourite country for zoo-visiting; I agree with Cat-Man’s comments.
If you stayed in Cologne then, as well as Cologne Zoo, you could visit the zoos in Duisburg, Krefeld, Wuppertal, Dortmund and Munster all of which can be easily reached by public transport from Cologne; the Dusseldorf Aquarium, too, is within easy travelling distance.
Another possibility is staying in Stuttgart; in addition to Stuttgart (Wilhelma) Zoo, you could travel to Frankfurt, Munich and Nuremburg on day trips (although the journeys are longer than those in the Cologne area).
Another suggestion would be to stay in Hamburg; as well as Hamburg (Hagenbecks) you could travel to Hannover and Walsrode.
My favourite, though, would be to stay in Berlin and visit both the (West) Berlin Zoo and the (East) Berlin Tierpark; these are, without doubt, my two favourite zoos in the world. Travelling to Leipzig from Berlin would be possible too, but at least two days are needed in each of the Berlin zoos to see them properly (and I've often spent three days in each zoo and never felt that I've spent too long there).