Agonised about US city (3,5)
I believe the answer is:
san diego
'us city' is the definition.
(I've seen this before)
'agonised about' is the wordplay.
'about' is an anagram indicator.
'agonised' is an anagram of 'SAN DIEGO'.
(Other definitions for san diego that I've seen before include "Calif. naval base" , "Southern California naval base" , "Californian resort" , "Californian port" , "California naval port" .)