Cherished origins of royal and ancient tourist destination (5)
I believe the answer is:
petra
'ancient tourist destination' is the definition.
(Petra is an ancient city in Jordan)
'cherished origins of royal and' is the wordplay.
'cherished' becomes 'pet' (as in a pet project).
'origins of' indicates taking the first letters.
The first letters of 'royal and' is 'ra'.
'pet'+'ra'='PETRA'
(Other definitions for petra that I've seen before include "Ancient Jordanian city carved from rock" , "Picturesque city" , "Old city in Jordan" , "Burgon's rose-red city" , "Jordan's rock-hewn city" .)