I voted for Liberty Tree Tavern. It's a nice, cool oasis at mid-day.They have great food, relaxing atmosphere and a wonderful waitstaff.
If you were looking for counter service, I would have suggested El Pirata Y el Perico, even though it's a hit or miss on it being open. It's the better of all the counter service in the MK IMO. but again, it looks like you're looking for a table service place.
Or if you were looking for a quick lunch, I would say to go to The Lunching Pad in Tomorrowland and get a turkey leg.....can't beat that!