When we self catered, we bought cereal for breakfast and stocked up on things like cherry toms, preprepared carrots, apples etc, plus things for making sandwiches, juice boxes etc so we could take a fairly healthy packed lunch to the parks with us.
Supermarkets can be huge, and we enjoyed shopping in them, prices are very similar to uk, not really as cheap as we expected. Buy in bulk if you can, ( American fridges are very large!) otherwise you end up shopping every couple of days, which can get a bit tiresome when you just want to get home after a long day at the parks.
We ate out most evenings, then back to the villa for a swim and a glass (or two!) of 
. Veggies can be a bit hard to come by, depending where you choose to eat. But a lot a places will do sides of corn, salad, broccoli etc if you ask.
If you really need a veg hit, the best place is Sweet Tomatoes. It's a chain, with a bit if a canteen feel, but is fab! It has the biggest salad bar I have ever seen, with really great fresh salads, cheeses, leaves, toms, dressings, toppings. Then there are soups, jacket and sweet potatoes with 'fixings', breads such as simple pizza, corn bread, focaccia, a dessert and icecream station, real lemonade. It's all buffet style, all you can eat style.
It was very cheap - we signed up on the website before we went and got vouchers for $25 for a family of four including drinks. We loved it (even th kids who are usually much more into burgers and chips)
I'm very envious, enjoy your trip!