Copenhagen

City · c. 965 CE · in Europe

Capital of Kingdom of Denmark (965–1406), Kalmar Union (1443–1523), Denmark-Norway (1536–1814).

Luxembourg (963 CE): Capital of Duchy of Luxembourg (1429–1449).
Lin'an Prefecture (c. 961–1278 CE): Capital of Northern Song (961–1027), Southern Song (1028–1278).
Khajuraho (c. 960 CE): Capital of Chandela Kingdom (960–1311).
Amalfi (c. 960 CE): Capital of Republic of Amalfi (960–1033).
Awantipora (c. 960 CE): Capital of Utpala Dynasty (960–1002).
Vitebsk (974 CE): Capital of Principality of Vitebsk (1111–1187).
Kaifeng (c. 951 CE): Capital of Later Zhou (951–960).
Stockholm (c. 980 CE): Capital of Kingdom of Sweden (980–today), Kalmar Union (1436–1523), Swedish Empire (1612–1721), and 1 more.
Nantes (c. 947 CE): Capital of Duchy of Brittany (947–1491).
Rennes (c. 947 CE): Capital of Duchy of Brittany (947–1491).

Around the same time and place

Christianization of Kievan Rus' (988 CE): Vladimir the Great adopted Orthodox Christianity from Byzantium and had the people of Kyiv baptised in the Dnieper.
Trier (16 BCE – 1618 CE): Capital of Electorate of Trier (1333–1618).
Varangians to the Greeks (c. 800–1100 CE): Scandinavian traders and warriors travelled from the Baltic up the Neva and Volkhov past Novgorod, portaged to the Dnieper and sailed down past Kiev to the Black Sea and Constantinople.
Otto the Great (912 CE – 973 CE): German king who defeated the Magyars and was crowned emperor in Rome in 962; he was buried in Magdeburg.
Rouen (c. 922 CE): Capital of Duchy of Normandy (922–1071).
Arles (c. 936 CE): Capital of Kingdom of Arles (936–1378).
Baptism of Poland (966 CE): Duke Mieszko I accepted baptism, bringing Poland into Latin Christendom; the event is traditionally seen as the founding of the Polish state.
Stephen I of Hungary (c. 975 CE – 1038 CE): First king of Hungary, crowned in 1000 or 1001, who converted his people to Christianity; venerated as Saint Stephen.