Aztecs:
Templo Mayor
Berbers: Teloet Kasbah of Morocco, or Kasbah of Sfax
Bulgarians: Shumen Fortress
Byzantines: Trikala Castle
Celts: Castle Sween
Chinese: Jiayuguan Fortress
Franks: Chateau de Thil
Incas: Sacsayhuamán
Koreans: Geumjeongsanseong
Magyars: Eger Castle
Lithuanians: Kaunas Castle
Mongols: Ark of Bukhara (Chagatai)/Diaoyu Fortress (Yuan China)
Persians: Alamut Castle
Portuguese: Castelo de Leiria
Saracens: Citadel of Aleppo
Spanish: Alcázar of Segovia
Teutons: Cochem Castle/Meersburg Castle/Burg Altena
(9 Oldest Castles in Germany - Oldest.org)
Vietnamese: Co Loa Citadel
Vikings: One of those Ring Fortresses
Civs that will still use their current models: Britons, Italians, Japanese, Khmers, Mayans, Slavs, Tatars, Turks
Civs with to-be-determined models: Burmese, Cumans, Goths, Huns, Malay, Malians, and Ethiopians
Do post your suggestions below!