I'll try to give the best summary I can, but this is just one opinion so take it with a grain of salt.
Overall housing is pricey. If you live in Foggy, you're looking at $1100/month for an efficiency on average (though you CAN find some deals, just don't expect to find anything less than $900/month). If you take a roommate or two, obviously you can cut that down, but usually not enough to fit the loan budget of $725 for rent AND untilities.
You're better off looking further out on the Metro, preferably something in Virginia (Arlington, Alexandria, etc.). If it were me, I'd be looking for something on the Orange line. A lot of my class lives in Court House, Ballston, Rosslyn (a little pricier because its closer). Once you get out past Falls Church, the prices become more manageable, but its still not cheap no matter how you slice it.
Bottom line, if you've got enough savings to supplement the financial aid budget enough to get your monthly rent budget up to arouund $850-900, you should be fine in Virginia. If not, you either get a roommate, or check out some of the less nice areas of Maryland or SE DC. I'd really try to stay in Virginia or Foggy though if I were you.
By the way, GW is a fantastic school. no complaints at all. If you're considering coming, don't let the cost of living dissuade you.
Hope this helps.
GWU - Class of '07