The Rose City, so nicknamed for its pink sandstone (5)
I believe the answer is:
petra
(Other definitions for petra that I've seen before include "Old city in Jordan" , "Historic city in Jordan" , "Burgon's rose-red city" , "Long-lost city of Jordan rediscovered in 1812" , "A rose-red city - 'half as old as Time'! (Burgon)" .)