Again, if you want to have regular family lunch, try out one of these places that are also kids friendly.
Let's start with Vinodol offering Croatian food in nice ambience in the very center (Teslina 10). You may also try Grička vještica (A Witch of Grich) in Vraniczanyeva 6 for an experience of the authentic (somewhat modernized) cuisine of old Zagreb while you visit the Upper Town, or Kod Šime (Martićeva 62) near Kvatrić Square where you can have Croatian, Mediterranean and European meals.