Thanks for the replies.
We can't eat a lot of carbs so therefore we need a protein(meat) and veggies unless we want our blood sugars to sky rocket. Then later we have fruit with a protein for a snack and that would be hard to find at the parks.
Personally, I bring food every day. However, we have fairly complex dietary restrictions and I got tired of WDW taking 30 minutes to screw them up. I also don't really care where you eat food that you brought with you or purchased onsite since in the great scheme of things it isn't very relevant.
However - I've spent a *long* time perusing Disney menus in the hunt for things I can eat. If you'd like to eat something from an on property CS I can suggest:
MK, Cosmic Ray's - half a chicken, double veggie
MK, Cosmic Ray's - Country Vegetable soup
MK, Cosmic Ray's - Caesar Salad with Chicken (omit the bread)
MK, Pecos Bill's - Chicken Salad
MK, Columbia Harbour House - Chicken Salad
Fruit is available at a cart in liberty square, a cart in toontown and I think a cart in frontierland. You could have turkey leg with it - but I find those disgusting. I'd bring in cheese instead or nuts.
Epcot:
Liberty Inn does a chicken salad
Tangerine Cafe does assorted meats with hummus or lentil salad
Sunshine Seasons has some interesting salads (with beets and goat cheese or seared tuna for example) and (usually low-carb) soups
Back at the bakery in France you can get a nice cheese plate with fresh fruit
MGM is the armpit of WDW, and I haven't ever found much edible there.
AK:
There's a cart near Safari that does cheese and fruit plates.
Tusker House is a great call and they're happy to do double cooked veggie or cooked veggie plus carrot sticks (the cooked veg is usually green beans)
Flame tree does a half chicken that's tasty and not sweet, but the sides leave something to be desired carb-wise. I'd go with slaw or ask for a small side-salad.
There are options. The options get really boring over the course of the trip, because they're all really the same few options. I just thought I'd list some of them because it's handy to know where you can eat *something* that's safe.