You're likely going to have to share an apartment or room with others. Even an efficiency condo is going to rent for a lot more than that. Also, though you prefer Northwest, you may have to broaden your search to the suburbs.
You'll also have a lot of competition. Among the schools in Northwest (as you know) are George Washington, Georgetown, American University, and others.
Be sure to check with your school's housing department. They may have listings or sharing arrangements that you won't find elsewhere (such as on Craigslist--be very careful of Craigslist).
Hope that helps.