I go round an Italian city (5)
I believe the answer is:
turin
'an italian city' is the definition.
(I know that Turin is Italian)
'i go round' is the wordplay.
'go' becomes 'turn' (as in one's go or turn in a game).
'round' is an insertion indicator.
'i' put into 'turn' is 'TURIN'.
(Other definitions for turin that I've seen before include "First capital in 1861 of united Italy" , "Italian city with famous religious Shroud" , "N. Italian industrial city" , "Industrial city of Piedmont" , "City of northern Italy" .)