You are at the offices of the World Health Organization and its regional counterpart, the Pan American Health Organization. The entrance and an interesting round front is a bit further away at the corner of 23rd and E St. Across the park from the GZ, you can see a statue of Bernardo de Gálvez. Like many DC statues, he’s on a horse. Further to the south, the State Department occupies a very large building. Its main entrance is on C St NW, but this is about as close as you can get for cache.
There might be a range of country flags on those flagpoles, but not always. Where you're standing, you should be close to two classic DC call boxes next to each other (note the different designs) where a magnetic key holder could be hidden. For the history of DC's distinctive fire and police call boxes see: http://househistoryman.blogspot.com/2012/02/history-of-washington-dc-police-and.html
Read the hint for additional information, which you should definitely use to make a quick find if there are muggles about.
Congratulations to Corbeno for FTF in sleet and snow within an hour of posting!