How about something on the Boardwalk or at the Yacht and Beach Clubs? You can either walk to those or take a boat from The Studios/Epcot. Or, you can take a boat from Downtown Disney to Port Orleans Riverside or French Quarter. There's a sit-down restaurant at Riverside, and both have pretty nice food courts.
whispering canyon cafe at wilderness lodge is a boat ride away from mk and open for lunch and dinner. espn club, big river grille, and beaches & cream are all a short walk out of the international gateway at epcot.
we usually do flying fish on the boardwalk on our dhs day, it's an easy walk or a slow boat ride. just head toward the bwi. we've had great meals and fabulous service there every time. we also love to do citricos on our mk day.