For quick service in DtD I would have said Earl of Sandwich, but alas, it was closed for the new hotel construction. RIP :-(
Tortilla Jo's has a taqueria that is quick service and is very tasty. Naples (pizza) has a quick service option too, but I haven't tried that.
As for the hotels, White Water Snacks is probably my favorite quick service. They have really good nachos (among other things) and the atmosphere is very laid back and quiet. You can sit outside and see a bit of the bustle from inside DCA.