Not at home, going round US city no matter what (6)
I believe the answer is:
anyway
'no matter what' is the definition.
(I've seen this before)
'not at home going round us city' is the wordplay.
'not at home' becomes 'away' (I've seen this before).
'going round' is an insertion indicator (some letters go around others).
'us city' becomes 'ny' (short for New York).
'away' placed around 'ny' is 'ANYWAY'.
(Other definitions for anyway that I've seen before include "in spite of everything" , "Still" , "Whatever happens" , "In any event" , "However that may be" .)