This is perhaps the region I'm most fond of and which I believe has great potential for further inscriptions.
From the sites mentioned so far, I second Abraj Al Kuwait, Jerash, Kumbi Saleh, Mecca including the Mountain of Mercy (even though access for non-Muslims is an issue), Kom Ombo and Edfu, Dendera, Ras Mohammed NP, Ninevah, Nimrud, Haid Al-Jazil, Dar Al-Hajar as a Sanaa extension, Abydos, Old Dongola and perhaps Western Desert natural landscapes in general (apart from the White Desert, there's the Black Desert, Crystal Mountain, etc. with unique biodiversity too).
Here are some more proposals from the book Islam: Art and Architecture:
Ziyanids; Tlemcen has more buildings dating from the 12th to the 15th century than any other town in Algeria. With the exception of the Great Mosque built by the Almoravids in the 12th century, most of the city's medieval buildings strongly reflect the influence of Moorish (Muslim) Spain.
The monumental door of the ruined minaret of the mosque of Mansoura, at the site of the Marīnid occupation camp west of Tlemcen is worth mentioning too.
The site is unique in that it has largely retained its historical footprint, and many significant Islamic monuments have survived.
Tarin in Hadramawt, Yemen
High rise buildings with powerful irrigation systems; significant role along the "incense road"
Palace preceinct of Mshatta, Jordan
most lavishly constructed of the Umayyad palaces (although portal facade and ornamental lion lie in Berlin)
Khirbit al-Mafjar, Palestine
Umayyid period decorated palace; rose window with a complete guilloche pattern is an excellent example of early Islamic art; dome ornamentation and lavish statues can be found in the Rockefeller Archaeological museum; mosaic floors
Palace of Ukhaidir, Iraq
this desert palace is the best preserved of early Abbassid palaces
Abbassid mosques in Damghan, Siraf and Nayin, Iran
earliest surviving minarets in Iran; important trading points of Abbassid empire
Medina and Great Mosque of Sfax, Tunisia
experienced revival during the Aghlabid period; perhaps and ideal extension of Kairouan to better represent Aghlabid period
Ibn Tumart Mosque at Tinmal and the High Atlas Mountains, Morocco
fortress of the founder of the Almohads (1080-1130) + natural environs perhaps as a mixed site; or else a worthy extension of Marrakesh
Marabout pilgrimage sites, Morocco
Sidi Shashkal (the Pilgrimage of the Poor), City Walls Square and Sidi Boudhab in Safi
Ghazna and ruins of al-Askar at Lashkar-i Bazar, Afghanistan
Ghaznavids citadel, towers and winter palace; 10th century monuments and decoratrive cenotaphs in modern Ghazni