Looks round centre of Florence, not a pretty sight (7)
I believe the answer is:
eyesore
'not a pretty sight' is the definition.
'looks round centre of florence' is the wordplay.
'looks' becomes 'eyes' (eyeing is a kind of looking).
'round' becomes 'o' (round can mean a round object).
'centre of' means to look at the middle letters.
The middle of 'florence' is 're'.
'eyes'+'o'+'re'='EYESORE'
(Other definitions for eyesore that I've seen before include "Something ugly to look at" , "Ugly structure" , "mess" , "Hideous building" , "Something exceedingly ugly" .)