Luxembourg

City · 963 CE · in Europe

Capital of Duchy of Luxembourg (1429–1449).

Lin'an Prefecture (c. 961–1278 CE): Capital of Northern Song (961–1027), Southern Song (1028–1278).
Copenhagen (c. 965 CE): Capital of Kingdom of Denmark (965–1406), Kalmar Union (1443–1523), Denmark-Norway (1536–1814).
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).
Nantes (c. 947 CE): Capital of Duchy of Brittany (947–1491).
Rennes (c. 947 CE): Capital of Duchy of Brittany (947–1491).
Stockholm (c. 980 CE): Capital of Kingdom of Sweden (980–today), Kalmar Union (1436–1523), Swedish Empire (1612–1721), and 1 more.

Around the same time and place

Reconquista (718–1492 CE): Centuries-long series of campaigns by Christian kingdoms to take the Iberian Peninsula from Muslim rule, ending with the fall of Granada in 1492.
Founding of the Holy Roman Empire (962 CE): Pope John XII crowned Otto I emperor in Rome, the conventional start of the Holy Roman Empire, which lasted until 1806.
Trier (16 BCE – 1618 CE): Capital of Electorate of Trier (1333–1618).
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).
Algiers (944 CE): Capital of Regency of Algiers (1706–1830), Free French (1940–1943), People's Democratic Republic of Algeria (1963–today).
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.