According to:
http://gwired.gwu.edu/adm/visit/placetostay.html
there are two official GW hotels:

The George Washington University Inn and One Washington Circle Hotel.

Their web cites are http://www.gwuinn.com/index2.html
http://www.thecirclehotel.com/index2.htm

The reasonable hotels in the neighborhood are:
State Plaza Hotel (2117 E St)
http://www.washington-dc-hotel.us/state-plaza-hotel.php
or Holiday Inn Rosslyn:
http://www.basshotels.com/h/d/hi/hc/waswp

For the hotels around Washington see:
http://www.180096hotel.com/cgi-bin/pickinput?SID=YDL&LKF=YDL&Dest=WAS

For Hotels in Bethesda see:
http://travel.yahoo.com/p-hotel-476388-bethesda_hotels-i