Hi,
My whole family (3 kids and hubby) are vegetarian.
We find quite a few restaurants have at least one lacto/ovo, vegan option. We went to Chef Mickey's character breakfast last year and one of the chef's walked us around the buffet and told us what was"safe" for us to eat.
There are a good amount of veggie burgers around property for a quick bite, most places have something veggie available but you will sometimes have to ask instead of seeing it on the menu.
It is great that everyone is so accomodating. Our family is waiting for the day when they offer veggie dogs!
Good Luck
Kristin