Singular or plural? One well-known institution with multiple locations.

Should "consulate" be singular or plural in the following?

1. John was an officer at the U.S. consulate in Shenyang, Vancouver, and Rio.

2. John was an officer at the U.S. consulates in Shenyang, Vancouver, and Rio.

My intuition is that both sentences are correct, but I cannot point to any concrete grammar rules to explain why. We can say "I went to the Hilton in London, Paris, and Berlin," right (we don't need to say "Hiltons")? Are both sentences correct and why or why not?