capital city

noun3

1. •
   A city that is a seat of government.
2. •
   A city (or cities) much larger or more important to a country than all others, regardless of the actual seat of government (cf., Moscow and Saint Petersburg regardless of moves of the Russian government; Amsterdam despite the Dutch government having been situated in The Hague since 1588).
3. •
   (Australia) The major metropolitan areas of Australia (Sydney, Melbourne, Brisbane, Perth, Adelaide), all of which happen to be state capitals, and by extension the major metropolitan areas of other countries; note that other state capitals Hobart, Darwin, and national capital Canberra are often excluded.