My son is 6 and a picky eater..here are some of the non-character restaurants he enjoyed...
Prrme Time 50's (DHS)
Via Napoli (EPCOT - he loves spaghetti)
Liberty Tree (MK)
Biergarten (Germany EPCOT - lots of music and loud and fun)
Morocco (EPCOT - Belly dancer and music keeps them interested and they have good child menu choices)
Whispering Canyon (Wilderness Lodge)
Ohana (Polynesian)
Though these restaurants don't have characters a common thread for most is that they are somewhat loud and have other things to interest younger kids (TVs in Prime Time 50's, etc.)
Tappen Edo may also be good as they prepare the food in front of you. Coral Reef has the large aquarium that is fun to watch. DS also was fine in Kouzzina (Boardwalk) and Kona (Polynesian) when he was younger. All the restaurants have coloring activities to keep kids busy plus we also bring a few busy items with us. With younger kids I would just stay away from the signature restuarants as they can be a bit more "elegant" and more geared towards adults. Since I know guests are paying more for these dining experiences I think it's best not to bring my young son as I wouldn't want to disturb the atmosphere for them with a child that may be loud. It all depends on what your kids like...