I agree with the PP about Wine Country Trattoria in DCA. Even though have always eaten outdoors there, they do have indoor seating. The food is not too overpriced, but the portions (especially the pizzetta salad) are generous. As far as a counter service place in DCA, I think Taste Pilots Grill is good. Not only do they have good food, but it is a place to go inside and escape heat.
In DL, I won't recommend Carnation Cafe or Bengal BBQ because there is no escaping heat at either of those places, but lots of people like the Plaza Inn (it's very pretty inside). River Belle Terrace is good too, and reasonably priced, and it is in a good location. Blue Ribbon Bakery is good for a blended mocha or a sweet snack IF you can get a seat inside.
In DTD, I like Rainforest Cafe (indoors or out), ESPN Zone (not exactly a 'relaxing' atmosphere because it is very busy and noisy due to the games on TV, but the food is great and it is cool inside) and Naples (eat indoors or out).
I also like Storytellers Cafe in the GCH (not the buffet, just off the menu) for lunch or dinner. They have good sandwiches and burgers that won't break the bank at lunch.
And I am a big fan of Goofy's Kitchen breakfast in the DLH, but I don't know if you are interested in any of character meals. Even though the food is usually great at these buffets, you can't really relax at any of the character meals because characters are constantly coming by to visit you. You kind of have to be alert at all times. And if you are watching how much you spend and trying to save money, the character meals are pretty costly. But if that is something you are interested in, then I say Goofy's all the way!