This is an impossible question. It allows for too many variables. Consider:
Does she cook? That is, would she prepare casseroles and healthy meals, or would she eat expensive, sodium-laden Lean Cuisines all the time?
If she cooks, what kind of cook is she? That is, does she know how to make inexpensive spaghetti sauce from canned tomatoes, or would she buy things like Hamburger Helper because they're easy?
If she's the type who'd make up a big yummy lasagna and salad on Sunday afternoon, would she then eat leftovers 'til it's gone, or would she let it sit 'til it goes bad?
Would she cook and share with roommates, and -- if so -- would they share fairly or would one roommate take advantage of the other? Would she have guests on a regular basis who would eat up her food?
Would she actually cook, or would she have good intentions but end up ordering pizza a couple times a week?
Does she have access to a low-priced grocery store, or would she find herself stuck buying overpriced items at the only grocery store to which she can walk?
Does she have a good handle on bargain-shopping, or would she pick up ridiculously expensive items like 100-calorie snack bags because they appear to be "right" for a college student on the go?
Does she have basic cooking items like frying pans, good knives, even some niceties like a food processor, etc., or would that be an added expense? True, these are things she will then have for the future, but you're probably the one who has to cough up the money now.
Does she stay on campus most weekends, or does she come home frequently? The real question is, does the budget have to stretch for 5 days or 7 days?
Will she stick to a budget that you give her, or will she wheedle and beg for more?
I'd say the answer to "How much would it cost?" is too vague to be answered. If she bargain shops and takes turns cooking big, healthy meals with fair-minded roommates and always carries her own drinks to class in a Tervis tumbler, she could end up spending as little as $50/week. On the other hand, if she warms up deli foods most nights, buys lots of snacks, eats out a couple times a week, and buys breakfast on the way to class every day along with the occasional Starbucks coffee, she could easily top $150/week just for herself.
I'm sure my own daughter would not save money cooking for herself. Her meal plan costs $1220/semester, which boils down to $87/week. She's not a cook. She would buy pre-made salads and Stouffers' mac-and-cheese all the time, neither of which are budget options. At 19 she's finally showing some interest in learning to cook, but she is more interested in moderately-expensive dishes like a knock-off of PF Chang's lettuce wraps rather than pinto beans and cornbread. She eats pretty healthy, but her idea of a perfect snack is fresh strawberries from Harris Teeter or edaemae hummas with homemade pita chips.
My daughter's staying on campus next year (her sophomore year) because she has loved the convenience and because she cannot live anywhere else as cheaply. However, she's already saying that when she's a junior and begins student nursing, she'd like to move off campus. Food is a part of that decision. Once she's doing student nursing, she won't want to be tied to on-campus food, and I agree that it'll make sense at that point -- when she'll be away from campus roughly three whole days a week -- to use the money for a meal in the hospital cafeteria or to be able to make a sandwich in her own apartment. I'm sure, however, that -- given her habits -- she will spend more than she does now on a meal plan.