One cheeky girl in Washington city (7)

I believe the answer is:

wichita

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'city' is the definition.
(Wichita is an example)

'one cheeky girl in washington' is the wordplay.
'one' becomes 'i' (Roman numeral).
'cheeky girl' becomes 'chit' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in' is an insertion indicator.
'washington' becomes 'wa' (two letter abbreviation for the state).
'i'+'chit'='ichit'
'ichit' inserted within 'wa' is 'WICHITA'.

Can you help me to learn more?

(Other definitions for wichita that I've seen before include "Kansas city" , "US city" , "city in America" , "place in Kansas" .)

I've seen this clue in The Independent and The Sun.

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