One cheeky girl in Washington city (7)
I believe the answer is:
wichita
'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" .)