I stayed at the Harrington in downtown. Its a block from the metro blue line which will take you straight to GW (3 stops) and Reagan National (like 8 stops). The hotel is a bit old but its safe, has a restaurant downstairs, an ESPN Zone across the street, and very friendly staff. Also its like 2 blocks from the mall if you want to do a little sight seeing.
Ran us 100/night but that was cheap compared to a lot of the other stuff I found.