Easter Market is one of the most authentic and original places for breakfast and lunch in DC. It is advisable to go on weekdays (weekends are full and you will hardly ever find a space). Besides various omelettes accompanied by potatoes, this place is famous for its delicious blueberry pancakes (you can order two or three at a time as they are served warm with maple syrup). This place couldn't be more American. Local rules include not allowing you to read the paper or use your laptop when it is busy.
Located on a small square just steps from Dupont Circle, the Farmer's Market is a small market held every Sunday morning. There is lots of fresh produce and organic fruits and vegetables too. There's also meat, fish, etc. In short, it's a great place to find food that comes directly from the producers.