Zurich has two botanical gardens: the "New" and the "Old" -- both part of the University of Zurich.
The larger new one opens summertime until 7pm and wintertime until 6pm, at Zollikerstrasse 107, with free admission. Instead of being arranged in systematic beds, most plants are wild species, with no effort to show garden hybrids. 'Bubble' green houses, a water garden and a useful plants garden are part of the layout.
The smaller old garden is now a public park at city center. At the high ground of the park is an old herb garden with around 50 sorts of medical plants. Also here is the Palm House pavilion. It's a great place to picnic or just to get away for peace and quiet.
Also here is the Ethnology Museum, (Völkerkundemuseum) of the University of Zurich, amid moats of the old city fortifications. The social, technical and philosophical achievements of many cultures are featured in ever-changing exhibitions. From Hauptbahnhof take tram 6, 7, 11 or 13 to Rennweg stop, and walk 200 meters down Pelikanstrasse.