cheezz, It will be very hard to get reservations in DC. I do know of a pretty cheap
motel in Arlington a block or so from the Metro in Clarendon. Mario's, a pizza-sub joint next door was one of my old high school hang-outs. Lefty still works the grill to make a dang great steak n' cheese with pizza sauce and hot peppers!!
The Highlander is an old motel, and probably pretty cheap for the neighborhood -- I won't vouch for security (but all rooms face the boulevard) or the ubiquitous bedbugs.
If she is alone and wants to stay in dc in a hostel, she'd be wise to stay in NW dc -- duPont circle is ok, woodley park is a good area.
Good Luck!!
Highlander Motel
3336 Wilson Blvd
Arlington, VA
703 524 4300