Go there even if you like meat
I'm no vegetarian. I don't think I've ever turned down a steak dinner in my life. But, I always try to visit Hiltl when I'm in Zürich: the dishes are interesting, the ingredients are fresh, and the variety is so great, everyone in our group can find something to eat there.
The place does get busy, so it may not be the best choice for a romantic dinner or a quiet conversation. For a more casual, faster vegetarian experience, check out Tibits by Hiltl restaurants around Switzerland.