This always-bustling cafe in Georgetown is one of my favorite places in the city. La Madeleine is part of a chain, although this is the only location I've ever been to. If you can get over the fact that you will probably have to wait in line for a good 10-15 minutes just to order (for some reason there is only one cashier), you will not be disappointed by the food. Their tomato basil soup is amazing, although if you go during the lunch hour rush, could very well be out. I usually get a croque monsieur (French version of a ham and cheese sandwich) with a side of pesto salad, and a potato galette, which ends up being a little less than $10. The chicken friande is also very good (a flaky pastry with chicken and mushrooms baked inside and covered with mushroom sauce).
I should mention that the above dishes are ordered cafeteria style. If you order breakfast items, any of the crepes, or dinner items, then you will pay the cashier, get a numbered wooden block and wait for your food to be brought to your table. It is not the most efficient system, but I think the food and prices make up for it. While most people know it as a breakfast/lunch place--I forgot to mention the free bread slices they put out, along with butter and jam that you can help yourself to--they also offer what I think are great dinner deals as well. You can get various pasta dishes, rotisserie chicken, or salmon with sides like mashed potatos, salad, green beans, all for under $14. They don't offer it anymore, but they used to serve a great beef tenderloin with mashed potatos and green beans.
La Madeleine is not a good place for large groups. The tables are small, close together and I don't recommend sitting on the first level near the door during winter time. If you happen to come in mid afternoon or another "off" time, (I still haven't quite figured out when that is) it is one of the coziest places to sit with a cup of coffee, enjoy breakfast and watch all the people going past on M Street.