For a wider listing of diplomatic entities, consider using Open Street Maps.
For example, you can use the Tag: amenity=embassy. This data source includes the following dimensions:
The dump that you want is wb_items_per_site.sql.gz. Though it contains mapping between article titles and wikidata ids for all wikis, so it's relatively big (~600 MB compressed).
And it's an SQL dump, so you can either import it into a MySQL database and query that, or you can try to parse it based on the unspecified (but reasonably stable) format.
Official lists maintained by government bodies:
The dc.gov (Washington, DC) has a dataset for all embassies in Washington, DC:
This data.gov dataset lists all US embassies/consulates in the World:
This open.canada dataset lists ...
Wikidata has a lot of data about embassies and consulates.
I wrote a SPARQL request to download the data:
Go to https://github.com/nicolas-raoul/database-of-embassies
Press the link called "Click here to see the data or download it" (the SPARQL request is so big I can not paste it here).
Press the "Play" button at the left.
Waiting for about a ...
Approximately since April 2016 you can do it in this way:
SELECT ?item ?sitelink
?sitelink schema:about ?item .
# ?sitelink schema:inLanguage "en" .
?sitelink schema:isPartOf <https://en.wikivoyage.org/>
Just to detail my findings about Andrew's first link (embassies in Washington, DC):
The data file can be found at http://geospatial.dcgis.dc.gov/dc_kmz/Culture_and_Society/DCG9_Miscellaneous_EmbassyPt/DCG9_Miscellaneous_EmbassyPt/DCG9_Miscellaneous_EmbassyPt.kmz
Once unzipped, open the doc.kml file, it contains such an item for each embassy:
How you can improve it depends very much on how you want to use it, and who you want it to be useful for. 'Valid' RDF is fine, but may not be useful depending on your intended application! If you want it to be helpful to open/linked types, publishing it using other 'accepted' vocabularies is good (although schema.org is the best catch-all, it is not always ...
What you can do is to create another entity that represents Abbeville, set it as schema:location (or maybe schema:containedIn?) of the restaurant and then use schema:sameAs to link to that Wikidata URI: