Palermo

City · c. 850 CE · in Europe

Capital of Emirate of Sicily (850–1091), Kingdom of Sicily (1139–1266), Kingdom of the Two Sicilies (1815–1860).

Kashgar (c. 850 CE): Capital of Kara-Khanids (850–1045), Eastern Kara-Khanids (1046–1138), Western Karakhanid Khanate (1046–1084), and 4 more.
Balasagun (c. 850–1218 CE): Capital of Kara-Khanids (850–1045), Eastern Kara-Khanids (1046–1138), Western Karakhanid Khanate (1046–1084), and 1 more.
Gangaikonda Cholapuram (c. 850 CE): Capital of Chola Empire (850–1259).
Sibenik (860 CE): Capital of Kingdom of Croatia (926–1098).
Beiting (c. 860–1138 CE): Capital of Qocho Kingdom (860–1138).
Brunswick (861 CE): Capital of Duchy of Brunswick (1815–1870).
Zaranj (c. 861 CE): Capital of Saffarid Dynasty (861–899).
Smolensk (863 CE): Capital of Principality of Smolensk (1056–1406).
Samarra (c. 836–892 CE): Capital of Abbasid Caliphate (836–892).
Olbia (c. 866 CE): Capital of Giudicato of Gallura (866–1209).

Around the same time and place

Coronation of Charlemagne (800 CE): Pope Leo III crowned Charlemagne emperor in St Peter's Basilica on Christmas Day, reviving the imperial title in the West.
Cyrillic script (c. 893 CE): Scholars in the First Bulgarian Empire, probably at Preslav, built a Slavic alphabet mainly from Greek letters; Cyrillic now writes Russian, Ukrainian, Bulgarian, Serbian and many more.
Trier (16 BCE – 1618 CE): Capital of Electorate of Trier (1333–1618).
Prague (800 CE): Capital of Duchy of Bohemia (896–1002), Kingdom of Bohemia (1202–1528), Holy Roman Empire (1346–1611), and 4 more.
Nitra (c. 814 CE): Capital of Principality of Nitra (814–839).
Heraklion (c. 830 CE): Capital of Emirate of Crete (830–960).
Jaca (c. 830 CE): Capital of County of Aragon (830–921).
Treaty of Verdun (843 CE): Treaty dividing the Carolingian Empire among three grandsons of Charlemagne, roughly foreshadowing France, Germany and Italy.