If you mean the best coffee to drink (and not the best café/best atmosphere or décor in Zurich) I have the answer: La Stanza. in Bleicherweg If you, instead, are referring to the whole experience of having a good coffee, there are many more places I can name, even though I don’t know all of them. Two classic places I love are Sprüngli, in Paradeplatz, and Motta, in Limmatquai 66.
Before answering I googled this questions and saw a lot of local articles with great pictures. But many times, in a typical Zurich way, the coffee itself looked terrible. Swiss people often love a certain place and location, and aren’t really interested in the quality of its coffee, or aren’t that fussy about it. But to me, being Italian, is it very important, and I cringe just looking.
How to spot a bad coffee? Bubbles/holes/air on a cappuccino foam, or a flat , watery espresso surface without the creamy, hazelnut brown layer one sees on a good coffee.
Also, since a good coffee can be made only by a continuously used coffee machine, I tend to stay away from hotel coffee. It might sound obvious, but a packed, busy place is often a place with a good coffee. On that note, there is another Zurich classic to try: Vicafe in Bellevue. I have never seen so many people queueing up for an espresso!