A good example of what I'm looking for is the Netherlands.
For most of the world, the Netherlands' premier city is 'Amsterdam'
Yet when you visit the Netherlands, you realize that The Hague is far more important than most would assume given brand name.
The Hague is...
1. The seat of the Dutch government (the Binnenhof is here, home to the Dutch equivalent of Congress)
2. The Maurithuis, considered one of the most important art museums in the Netherlands, perhaps only second to the Rijksmuseum
3. The home of the Peace Palace, which houses the International Court of Justice (which is the principal judicial body of the United Nations) and the International Criminal Court.
4. The home of the Dutch Royalty, with King Willem-Alexander living in Huis ten Bosch and working at the Noordeinde Palace
5. A major beach resort, with palatial hotels on the coast like the
Kurhaus
6. It lies in between Amsterdam and Rotterdam, making it a major transport link within the Randstad
7. A major corporate hub, and headquarters of Royal Dutch Shell
Of course, Amsterdam vastly overshadows any other Dutch city, so you'd think it were the undisputed primate city of the Netherlands, when in reality it's far less important within the Netherlands than outside of it.
What other cities have this dynamic?