I agree with the other posters, that the online menus are a great way to estimate your food costs.
However, if you're just looking for a ballpark estimate:
Counter service adult entree + side = $6-7
Adult soft drink = $2 - $2.50
Kid's meal including drink = $4-6
So, I'd probably estimate $9 adult, and $5 per child, per meal. If you're looking to save money you could probably do some things like share a large drink instead of ordering two smalls, or share a meal that has big portions. When we went in december (me, DH, DS7, DD3), I overestimated because I budgeted for everyone to get their own meal each time, but we ended up sharing several times. But, don't forget to budget for a few snacks here and there. Our favorite (mickey mouse ice cream bars) are $2.50 each.