[Spirit of Liberty]

Doesn’t appear to be a stadium.

Not that it couldn’t have been; it put me in mind of some of those Gothic-style stadiums some colleges have, like University of Notre Dame or maybe Florida State University.

You don’t often see the Eisenhower Executive Building behind the West Wing in a photo; usually the shot angle is too low.

[Slicksadick]

The two chimneys on the left seem to match the SW corner of the Eisenhower Executive Bldg, across the street, west of the White House