An extremely nice (and often overlooked) place to eat lunch is at the Plaza Restaurant (not the Pavilion). The restaurant is really charming, cool on a hot day and they make the BEST sandwiches. Give it a try!
I'd suggest Cinderella's Royal Table for a very cool, relaxed lunch with some good, different choices. And it's always a treat to dine in the castle!
Also Liberty Tree Tavern has a very good lunch too.