I concur that the two-block walk to Union Station is just fine. Cross the mess of streets in front of the station (1st, then Mass) and walk down E St. Cabs are a menace, sure, but email has largely obviated bike messengers. Traffic is a lot lighter around there than in the core of downtown to the west.

The walk to Judiciary Square is sketchier but still harmless, since it passes a homeless shelter.

As for the hotels, I've only stayed at the Hyatt, which was fine; can't comment on the Liasion or Affinia in general. They are indeed right across from one another.