Sorry, no spare room, and not all that close to Alexandria, either. Something to realize about the DC area is that, due to the joyous traffic snarl we have (last I heard, we ranked 2nd to Los Angeles... and it was close), 30 or 40 miles can be a long trip. I'd suggested you focus on Alexandria & Arlington, though it'll be a bit spendy. You might find something in Fairfax, and you may want to consider looking in MD, too. A lot depends on exactly where you'll be, too. If you're at the Coast Guard base off Telegraph Road, you might look at eastern Prince William County, too, but if you're at the Pentagon? Some of those same places mean an hour plus travel time each day... You can probably find places available via eBay and Craig's List.
I'll see if there are any rooms posted at the police academies in the area.