I would also recommend Rancho Del Zocalo. We were able to share meals there and were all pretty full. Since you are bringing snacks (and going when it can be hot) I would bring your own bottled water. Water is $2.75 to $4.50 a bottle (I was just there Sunday and forgot to bring water as we usually do). This will help keep your budget in line if you bring water yourself, as well as your own snacks.
If you are interested in a character meal, we just checked out Ariel's Grotto in DCA. We went for lunch and the adult lunch was $14.99 and the kids was $10.99. I know this is more than a regular counter lunch, but the food was pretty good and the kids loved the characters!! The kids also got their own pail and shovel to take home. Make sure you make a PS here as the line can be long!!!!
As a treat for ourselves, as well as a cost saver, we try the sit down places at lunch, and eat counter (or outside the park) for dinner. We just find that it is a nice break in the middle of a hot day to be able to do a sit down meal and take a break, then back to commando the rides. Have fun!!