I would let the school find your accommodation hoping that they could find a safe place and not far from school. Don't try to save money. Washington DC is not a safe place and you do not know the area well. The Metro (subway) is not cheap so you must take into account the cost of transportation. I lived in Maryland and working in Washington DC for 7 years. During that time a Thai student was murdered walking around Dupont Circle. You have to be careful all the time.