For food, since you mention on the cheap, most of the time you can actually split one meal, and it's enough for 2. The food at the parks usually costs more, but when you eat at a sit down type place, the portions are huge. This works well for my wife and I for lunch, and sometimes breakfast (when we eat it), saving money for a nicer dinner. For example, my wife and I got a double hamburger, fries, and drink at Pecos Bill's in the Magic Kingdom, paid about 7 bucks or so, and it was damn enough for 2. Just over 3 bucks to eat there is pretty good. These types of places are in all 4 main parks.
Also make sure to try allears.net and mousesavers, which have already been mentioned.
Stay on the resort at one of the "All Star" resorts, or even off property near Downtown Disney, the busses save you a car rental.
If you know you are going back someday, you can spend a bit more and make your park hopper passes never expire. It doesn't save you much on the front end, but for every day you add, the cost of admission goes down, so next time, you can subtract park passes.
If you are carrying a backpack, take a couple of plastic drink cups (the kind with handles and a lid). If you really want cheap, free water from fountains, and I don't think they charge you for ice, or they didn't used to.
Spiritseed, do you know how lucky you are, in my eyes anyway, to live down there?
Someday I hope to.