'airy thing maybe hopping about capital (9)
I believe the answer is:
amsterdam
'capital' is the definition.
(Amsterdam is an example)
I don't understand the rest of the clue.
(Other definitions for amsterdam that I've seen before include "place of canals" , "Dutch port" , "European capital" , "City of the Rijks-museum and Van Gogh Museum" , "diamond-cutting centre" .)