It is just beside the name of the county, on the top left corner, looks like a small crown button.
As for changing the county capital, the owner of both the current capital and the one that wants to become so need to be the same. So if you want to own it yourself, but dont want to be, say, a city, you'll need to grab one of the castle within the county. The game will then switch it on its own based on what you are (Feudal=Barony Republic=City).
And if you dont want that county for yourself but dont want a wrong-type vassal, just give the county to whoever currently holds to proper type holding in that county. Example, if it is currently a city as capital but you are a feudal lord, give the city to the current baron of the castle in that county. His Barony will then become the capital on its own and he'll probably vassalize the city you just gave him.