At MK, we like the Liberty Tree Tavern and Columbia Harbour House. You should definitely check the menu site that someone above posted as your family may not like the choices at those 2 places. As someone above noted, Liberty Tree Tavern has good home-cooking meals. I think dinner there is with characters served family style. We are going there for lunch. I think lunch is normal table service.
At Epcot, there are a million choices. We personally love LeCellier (filet mignon!) in Canada. We are eating at Alfredo in Italy next month. We like Nine Dragons in China. So whatever kind of food your family likes (Italian, steaks, chinese, etc.), you will most likely find it in Epcot!