As with others, it will really depend on you....disneysteve manages to feed his family on less than $20 per person per day - IIRC, lots of offsite meals, lots of cooking in their condo, some sharing, no alcohol. We spend $20 a day in umbrella drinks watching the kids in the pool. Some families budget carefully, choosing one snack and sharing. Others get four Dole Whips, throw away most of them, and are picking up four funnel cakes when they hit Liberty Square. Some people will order a $100 bottle of wine with their four course dinner, others will split a double burger with an extra bun at Peco's Bills. Some people skip a character meal in favor of visiting characters for free in the parks (or skipping the character experience altogether), other people schedule four or five character meals in an eight day trip at $100+ a pop for a family of four.
There are two ways to go about this. One is to decide what you want to eat (check out the menus on allearsnet), figure out what it will cost you, and cut back from there as necessary. The other is to figure out how much you can spend, then plan your meals around that. If your budget is tight, hop over to the budget board for hints to stretch it.
hint one, Disney doesn't care if you bring in your own bottle of Diet Pepsi and a few granola bars or whatever.
hint two, most sit down restaurants are cheaper for lunch. The portions are sometimes (not always) smaller - and the menus are sometimes different.