Cafe Ferdinand: Gutstrasse 2, Zurich 8055
The resturant isn't fancy, but the food is very good, and it's family run. You can take trams 9 & 14 to the stop after Goldbrunnenplatz (I believe the stop is Talwiesenstr, but not 100% sure) and it's right there on the corner.
As for Ayran, I recently saw this being sold at Migros near the milk and cream. Haven't tried it, since I'm not a fan of yogurt though.
There is also another good Turkish resturant in the Niederdorf called Klein Istanbul that I can also recommend.
There's also this:
Turkish Restaurants