Charles,
So all of these are great, but if it is you and your daughter, it has to be perfect. Of these, I would bring it down to either Jiko or the Yachtsman Steakhouse. My choice would be Jiko, but here is why I pick these two;
Jiko is a phenomenal meal. Probably one of my three favorites on property. While the dining area is not 'festive', it is starkly beautiful. More importantly, your daughter will find the host resort (The Animal Kingdom Lodge) to be a memorable place to visit. Checking the animal savanna out back, even after dark, is pretty amazing.
Yachtsman Steakhouse is also a great meal, and being in the midst of the BoardWalk/Beach Club/Yacht Club area is fun too. You could combo dinner with ice cream either at the BoardWalk or at the even closer Beaches and Cream.
There is nothing wrong with Narcoossee's, Artist Point, or Fulton's, but I think those two are the best of the 5 choices.
Write me back if you have any follow-up questions!
Have a magical (and delicious) vacation!