Bad hair day, having abandoned a city in the Middle East (6)
I believe the answer is:
riyadh
'city in the middle east' is the definition.
(Riyadh is the capital of Saudi Arabia)
'bad hair day having abandoned a' is the wordplay.
'bad' indicates anagramming the letters.
'having abandoned' indicates named letters should be taken away.
'hair'+'day'='hairday'
'hairday' with 'a' taken out is 'hirday'.
'hirday' is an anagram of 'RIYADH'.
(Other definitions for riyadh that I've seen before include "Capital city of Saudi Arabia" , "Saudi Arabian capital" , "Saudi Arabian city" , "Capital of Saud Arabia" , "Middle Eastern capital" .)