I agree with ahales that the SW Waterfront area is probably his best bet, especially around 6th or 7th Street. If he can't find anything affordable there, HUD is on top of the L'Enfant metro station, so he can try to find a place near a metro line (yellow, green, blue, and orange all go there, go to
Metro - Rail - Maps - Rail/Google Map) and take that in.
As far as "cheap", that's pretty relative. A studio apartment can easily run $1200 in the DC area, which is astronomical compared to some other areas of the country.