What is your criteria for a small apartment?
I thought a lot about what you're asking, and DC just isn't built that way as strange as it may sound.
High rise? You'd have to be in Crystal City or Rosslyn for that.
Super busy area, as to be discrete?
No doorman condo security?
Metro accessible? Easy Parking? (Easy parking and free excludes pretty much the whole city unless you own a house).
Nearby amenities? Restaurants?
There are some upcoming residences near the convention center and on Mass. Ave. near "G" street corner, kind of near Union Station.
A safer area is near DuPoint but traffic is absolutely horrific the hours you'd be wanting to host.
As mentioned, I'd target the "K" street corridor, but no lower than 11th Street. Then you're getting into the hood between 10th and 5th street area. Its being gentrified quickly, but not quick enough.