The obvious - head south to East Potomac Park or National Mall
You can follow the mall past the Lincoln Memorial, and run across Arlington Memorial Bridge to the Mt.Vernon trail on the Virginia side
Or you can head west from your hotel and hook up with Rock Creek Park at P Street. Heading south on that will connect you to the C&O canal or you can continue south also to the Memorial Bridge. Go north to more wooded trails, several miles north and you won't feel like you're in the city anymore.
If you're ambitious, go west a ways on the C&O and find Glover Archibold which is probably one of the best trails in the city. Also a way to get to this from Rock Creek, going through Dumbarton Oaks and through GTown -- but won't be easy for an outsider.
Up Massachusetts past Dupont will take you by the Embassies, which is probably one of the more decent runs you can do in the city on sidewalks.