Flying Fish for sure. The food is fabulous and the atmosphere is just so lively and cute. The potato wrapped snapper is absolutely incredible, the kind of dish you find yourself craving long after your trip is done and over with.
California Grill is a must-do for my family, but we can't get great sushi at home and it is definitely the highlight of their menu. If you aren't going for the sushi or the view you'd probably be better off looking elsewhere.
Jiko is also very nice, just a little exotic without being too over the top. I loved the ostrich appetizer, which I don't think is on the menu any more, and the short rib entree was excellent. It is a little quieter than most of the other signatures, but not so much so that a young child would be out of place during prime dinner hours.
Narcoosees was a hit with the lobster-loving members of my family but just pretty good for those of us who don't really go for lobster. They do, however, have my all time favorite Disney dessert, the almond crusted cheesecake.
Brown Derby really didn't feel like a signature to us, and I don't think it is worth the two credits unless you're going for the Fantasmic package (and that's mainly on the weakness of the other choices, not the strength of BD's offerings). The Cobb salad is to die for but the rest just didn't live up to signature status.
Yachtsman Steakhouse was quite good but at the same time not anything different than you'd find at any other good steakhouse anywhere in America. We enjoyed our meal there but really don't have any burning desire to go back because we can get a comparable experience here at home.
ETA: We've taken our toddler to all of the above except Yachtsman, which we tried on a trip before she was born, and never felt out of place for taking her anywhere. She was 16mo on her first trip and 2.5 on her second. That's one of the things we love best about Disney - in the "real world" having a toddler tends to limit your nicer dining options, but at Disney the only place where kids aren't welcome is Victoria & Albert.