Western city daughter avoided (6)
I believe the answer is:
dodged
'avoided' is the definition.
(dodging is a kind of avoiding)
'western city daughter' is the wordplay.
'western city' becomes 'dodge' (dodge city, kansas is known for the old west).
'daughter' becomes 'd'.
'dodge'+'d'='DODGED'
(Other definitions for dodged that I've seen before include "Quickly avoided" , "Evaded or sidestepped" , "Eluded" , "Moved sideways to avoid, say missile" , "Evaded by sidestepping" .)