Remains very unwell visiting north-eastern US city (9)
I believe the answer is:
nashville
'us city' is the definition.
(I've seen this before)
'remains very unwell visiting north-eastern' is the wordplay.
'remains' becomes 'ash' (remains of a fire).
'very' becomes 'v' (common abbreviation).
'unwell' becomes 'i'll' (similar in meaning).
'visiting' is an insertion indicator.
'north eastern' becomes 'NE' (abbreviation).
'ash'+'v'+'ill'='ashvill'
'ashvill' going inside 'ne' is 'NASHVILLE'.
(Other definitions for nashville that I've seen before include "country town" , "music centre" , "Grand Ole Opry city" , "Centre of country and western" , "US city" .)