The Animal Kingdom Lodge has a very nice 'counter service' restaurant, the Mara. It has many nice meals from the hot counter, depending on the time of day, and there are many things you can "grab 'n' go". I really like the Mara. However, it is not open 24 hours a day.
The Polynesian has Capt. Cook's, which was sufficient for our needs. It "is" open 24 hours, which I love, because I sometimes get up very early, and I like to be able to get coffee around 6 AM.
We stayed at the Contemporary way back, and from what I remember the "food and Fun" center was, again, adequate for our wants. I am not sure of their hours.