Alexandria wouldn't be a good option -- not very protected for anchoring and the King Street Metro stop is too far away. If you have bikes it might work, as might Washington Sailing MArina. WSM is immediately south of Reagan National Airport, you could walk or ride bikes (on a path) to the RNA Metro stop.
But BY FAR the best location for visiting DC is the one that WindMagic described. Good, protected anchorage, with easy
dinghy access to Gangplank Marina (they charge a small fee to boats that are anchored out, which gives access to the showers,
dinghy dock, etc) and nearby Metro stop. Heck, you can walk to many of the downtown attractions from there without even getting aboard the Metro.
On your chart, the basin in WindMagic's photo is located at the northwest end of the waterway called "Washington Channel". Washington Channel shares a common mouth on to the Potomac with the Anacostia River.
Just a bit further up Washington Channel, under that bridge (too low for larger sailboats but fine for powerboats and
dinghies), is another marina called Washinton Marina. They have a good chandlery, for outboard and auxiliary engine parts, marine supplies, etc. They are a dealer for Mercury, Honda, Yanmar, etc.