I feed kids all the time, and I'm all about cheap. The best deals on cheap food always tend to be things that are really bad for you, so what I do is stock up on the good things when they go on sale. A couple of weeks ago I bought boneless chicken breast on sale for $1.69/pound, around here that's pretty cheap so I bought 8 of the 6 pound bags. We go through about a bag/week give or take. My kids love chicken in just about any form, and it's one of those things you can make with or without extra calories. We probably eat Mexican once a week, usually the kids and DH get chicken tacos and I make a chicken taco salad for myself. The kids also like honey-nut-chicken sticks better than chicken nuggets, and when I make those for the kids I'll broil a breast for myself without the honey nut coating.
We also have the occasional home cooked burgers, especially now that it's grilling season. I just serve them on whole grain slim buns or whole grain English muffins, instead of the usual hamburger bun. Chili is also an easy meal, and if you sub in ground turkey instead of beef it's a lot lower in fat.
I also watch the weekly produce sales carefully. Our local grocery store runs sales Sun-Sat, and then they also sometimes have a Th-Sat sale on top of that. If lettuce goes on sale Sunday morning, I buy 2-3 heads and then hit the store again on Saturday and get more for the next week. Same with veggies, fresh fruit and dairy products when they go on sale. In the summer I take the kids to U-pick places, where they can eat all the fruit they want for free and then I freeze or can up whatever we picked but didn't eat. Around here you can also find farmers that sell farm fresh eggs, which tend to be cheaper than the grocery store full price. Eggs are really great to have on hand, they are good for breakfast, sandwiches and snacks. My oldest DD is now completely hooked on deviled eggs.
I like to get bread from the day-old bakery. They usually have the whole grain slim buns and the 35 calorie/slice whole grain loaf for $.69, instead of the $3.19 the grocery store charges. I've changed the whole family over to whole grain 35-40 calorie/slice bread, and every one of them has dropped a few pounds from it. We've also switched over to healthy cereals and skim milk, which was easier than I expected.