We usually spend about $40 day for two adults and a child. We visit during shoulder season, and find that what we tend to do is cut down to two meals per day, as stopping to eat just takes too much time away from ride time. I always carry protein-type snacks, especially nuts, they stick to your ribs pretty well. We don't really do this as a budgeting tactic; more that we prefer not to overpay for food.
We eat breakfast in our room, and that we purchase offsite. We always make sure that breakfast has protein, so we buy smoked meats that will keep well in a cooler in our room. (You want to double-bag those cold cuts and wrap the inner bag in napkins to blunt the cold somewhat; otherwise they will freeze.) For short trips I will carry the breakfast munchies down with me in my carryon soft cooler and just buy a few drinks at a convenience store; for long trips we check our hardside rolling cooler as one of our bags, and we do a full grocery store stop. (A full grocery stop for a week's trip will normally run ~$25 not incl. liquor. That's a separate budget item the way I calculate it.) We don't snack too often, so we are not talking a huge volume of food, mostly fruit, nuts and pretzel sticks.
We tend to eat sit-down meals more often than counter-service, as the quality is much better, but more commonly at resorts instead of in the parks. We always take a midday rest, so we will normally stop at a resort and eat either coming or going. We share our restaurant meals in some way or another, either by buying one adult entree and one kid meal, or just splitting 2 adult entrees three ways. We don't normally buy any drinks in the parks; we carry a couple of Brita bottles and just drink tap water. (I'm a cold-caffeine junkie, so I carry in a 16 oz. Coke that I've purchased offsite. I ask for ice and add the Coke to feed my addiction. I don't do this at meals, though, just during breaks.) All our snacks are carried in, with the exception of one Mickey bar per trip for DS.
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