Note repeated about a city in Florida (5)
I believe the answer is:
miami
'city in florida' is the definition.
(Miami is a city in Florida)
'note repeated about a' is the wordplay.
'note' becomes 'mi' (as in 'do re mi').
'repeated' shows that letters should be duplicated.
'about' is an insertion indicator.
'mi' doubled is 'mimi'.
'mimi' placed around 'a' is 'MIAMI'.
(Other definitions for miami that I've seen before include "I put out of action when returning" , "Popular sun-city of Florida" , "Florida resort city, Beach" , "place associated with vice?" , "Sunshine city in SE Florida" .)