Officially, Disney parks frown on bringing in outside food, and they won't let you bring in anything in a hard-shelled cooler. However, if you're discreet and don't lug an entire Thanksgiving dinner around, you can usually bring your own food into the park without a fuss. Sandwiches and snacks purchased at a local grocery store make a cheap and healthy alternative to buying food at the kiosks. Water and soda, too, can be bought inside in a backpack or purse. Disney parks have locker rentals to keep your food while you go on rides, allowing you to eat when you like without having to carry it around all day.
Disneyland in Anaheim is right in the middle of Southern California's suburban sprawl, which means there are a number of restaurants within easy walking distance. A mall directly across the street has a Subway, a pizza place and a Chinese restaurant, all available for about half the price of meals in the park. Disney World is somewhat trickier--a drive into Orlando may be entailed--but you can get your hand stamped and come back to the park when you're done. "Official" nearby locales like Downtown Disney have restaurants as well, often just a short trip away on the monorail.
Sit-down restaurants in the Disney parks are often extremely expensive. If you're going to eat in the park, try dining at kiosks or other walk-up locations. The quality is marginally lower, but you'll save both money and time. Another option is to feed two people with one meal. Portions are often very large at Disney restaurants, and you can easily get enough for a second diner, especially if it's a child. Avoid character breakfasts or similar gimmicks; they're very expensive. Instead, look for fruit stands scattered throughout the park, which are much cheaper and easier to fit into your schedule as well.
