Spin around one city (5)
I believe the answer is:
turin
'city' is the definition.
(Turin is an example)
'spin around one' is the wordplay.
'spin' becomes 'turn' (I've seen this in other clues).
'around' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'turn' enclosing 'i' is 'TURIN'.
(Other definitions for turin that I've seen before include "N. Italian industrial city" , "Italian city with sacred Christian Shroud" , "Piedmontese capital" , "Italian destination" , "regional capital" .)