Cheap time in New York (5)
I believe the answer is:
tinny
'cheap' is the definition.
('tinny' can be a synonym of 'cheap')
'time in new york' is the wordplay.
'time' becomes 't'.
'new york' becomes 'ny'.
't'+'in'+'ny'='TINNY'
(Other definitions for tinny that I've seen before include "Metallic-sounding" , "Lacking resonance" , "insubstantial" , "Of poor audio quality" , "Sounding thin and metallic" .)