[@Buddha]
Sorry, I feel we're talking at crossed purposes. Why does a mountain definitely mean the border of a province? There are examples of mountains in the centre of countries in real life, Ben Nevis for example, but this is a fantasy land. Obvious inspiration for a central mountain would be the Eyrie but there's also the Lonely Mountain or that mountain in the Inheritance cycle the name of which I don't remember but had a bunch of dwarves in it.

Personally I think a capital city at the base of a mountain is a cool idea, particularly as it lends itself really well to a deep cultural divide between those that live on the mountain and those that live at the bottom. Say if the mountain was seen as a holy location, like Mount Olympus, perhaps the people who live on it have less learning and shun technology but have a closer spiritual connection to the faith and are seen as holy men, while those at the bottom are often seen as soft and weak but control trade, commerce, politics and develop the most advanced technology of the era. There's a lot of stuff that can be done with that set up and it satisfies both parties in a tight vote.