Gone off to a city (5)
I believe the answer is:
genoa
'city' is the definition.
(Genoa is an example)
'gone off to a' is the wordplay.
'off' indicates an anagram.
'gone' is an anagram of 'geno'.
'geno'+'a'='GENOA'
(Other definitions for genoa that I've seen before include "Seaport in northwestern Italy" , "Italian city has no age, oddly" , "NW Italian sea port" , "Cake type; foresail" , "Type of rich fruit cake" .)