My family loves Via Napoli; really good food, fun atmosphere, nice servers. We were very underwhelmed by Tutto Italia...ok food and indifferent service on a very slow day.
We also like San Angel Inn, though as has been pointed out, it's authentic Mexican, not Tex-Mex and thus not to everyone's tastes. With the volcano and pyramid in the background, it has great atmosphere, and the boat ride you can take before or after is fun too, especially for kids.
Both Chefs de France and Coral Reef are on our 'we can go back' list...neither was amazing, but were enjoyable with good service and atmosphere. Coral Reef probably has the edge on atmosphere for kids.
I've never done Biergarten, but friends and family with kids have, and they've loved it. Haven't done Garden Grill, but have heard very good things about all meal services (breakfast through dinner)...it seems to be close the week we're going in December, as there is no availability at all this far out, which is highly unusual.
If you are a family of seafood lovers, you could always try to get an ADR for Cape May's buffet (in YC) at a time that would allow you to go back to Epcot for Illuminations. Cape May's nighttime buffet is really good, really plentiful, and my crab-leg loving cousins ate their weight in crab legs the last time we went. I think Dis lost money on our party that night we ate so much! The BC/YC resort is very close to the international gateway to Epcot, so that's an option to consider.
Good luck, and good eating!